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Quizzes > High School Quizzes > Mathematics

7.09 Trigonometric Functions Practice Quiz

Boost exam readiness with trigonometric angle review

Difficulty: Moderate
Grade: Grade 10
Study OutcomesCheat Sheet
Colorful paper art promoting the All-Angle Trig Challenge quiz for high school students.

What is sin(0°)?
 
0
-1
1
At 0°, the y-coordinate on the unit circle is 0, so sin(0°) = 0. This basic property of the sine function makes 0 the correct answer.
What is cos(0°)?
-1
 
1
0
At 0°, the point on the unit circle is (1, 0) so cos(0°) equals 1. The cosine function gives the x-coordinate, confirming that 1 is correct.
Which quadrant includes angles between 0° and 90°?
Quadrant II
Quadrant I
Quadrant IV
Quadrant III
Angles from 0° to 90° fall within Quadrant I of the coordinate plane. In this quadrant both sine and cosine are positive.
What are the coordinates of the point on the unit circle at 90°?
(0, -1)
(1, 0)
(0, 1)
(-1, 0)
At 90°, the point on the unit circle is (0, 1) because the cosine (x-value) is 0 and the sine (y-value) is 1. This is a fundamental coordinate on the circle.
Which trigonometric function represents the ratio of the opposite side to the hypotenuse in a right triangle?
Tangent
Cosine
Sine
Secant
The sine function is defined as the ratio of the length of the opposite side to the hypotenuse in a right triangle. This makes 'Sine' the correct answer.
What is sin(150°)?
0.5
0.866
-0.5
-0.866
The reference angle for 150° is 30°, and sine is positive in the second quadrant. Since sin(30°) = 0.5, sin(150°) is also 0.5.
Evaluate cos(225°).
√2/2
-1
-√2/2
0
225° is in the third quadrant where cosine is negative, and its reference angle is 45° with cos(45°) = √2/2. Hence, cos(225°) is -√2/2.
Find tan(135°).
-1
1
0
 
Tan(135°) equals tan(180° - 45°) which is -tan(45°). Since tan(45°) = 1, the value is -1.
Convert 300° to radians.
5π/3
π/6
7π/6
4π/3
To convert degrees to radians, multiply the angle by π/180. Thus, 300° × (π/180) simplifies to 5π/3.
Evaluate sin(-30°).
0.5
-1
1
-0.5
The sine function is odd, so sin(-θ) = -sin(θ). Since sin(30°) = 0.5, sin(-30°) = -0.5.
What is the period of the sine function (in degrees)?
360°
90°
180°
30°
The sine function repeats its pattern every 360° when measured in degrees. This periodicity means that 360° is the correct period.
Find the reference angle for 210°.
90°
30°
60°
45°
Since 210° lies in the third quadrant, its reference angle is determined by subtracting 180°: 210° - 180° = 30°. Thus, the reference angle is 30°.
Which trigonometric function is undefined at 90°?
Sine
Cosine
Cotangent
Tan
Tangent is defined as sinθ/cosθ, and since cos(90°) = 0, tan(90°) is undefined. This division by zero is why tangent fails at 90°.
If sinθ = 0.6 and θ is in the first quadrant, what is cosθ approximately?
0.8
0.6
1.0
0.4
Using the Pythagorean identity sin²θ + cos²θ = 1, cosθ = √(1 - 0.6²) = √(1 - 0.36) = √0.64 = 0.8 in the first quadrant.
Express tanθ in terms of sine and cosine.
cosθ/sinθ
1/(sinθ*cosθ)
sinθ * cosθ
sinθ/cosθ
By definition, the tangent function is the ratio of the sine function to the cosine function: tanθ = sinθ/cosθ. This identity is fundamental in trigonometry.
Calculate sin(510°).
-1
-0.5
0.5
1
Subtracting 360° from 510° gives 150°, so sin(510°) = sin(150°). Since sin(150°) is 0.5, the correct answer is 0.5.
How many solutions does the equation tanθ = √3 have in the interval [0°, 360°]?
4
1
3
2
The tangent function has a period of 180°, so within a 360° interval there are two solutions to tanθ = √3. This accounts for the answer of 2.
Evaluate tan(405°).
1
-1
√2
0
405° is coterminal with 45° (because 405° - 360° = 45°), and tan(45°) equals 1. Therefore, tan(405°) is 1.
For 0° ≤ θ < 360°, if sinθ = cosθ, what is the value of θ?
Only 45°
90° and 270°
45° and 225°
Only 225°
The equation sinθ = cosθ implies that tanθ = 1, which is true for θ = 45° and θ = 225° in the interval [0°, 360°].
Using the Pythagorean identity, if cosθ = -3/5 and θ lies in the second quadrant, what is sinθ?
3/5
-4/5
-3/5
4/5
Using sin²θ + cos²θ = 1, we get sinθ = √(1 - (9/25)) = √(16/25) = 4/5. Since θ is in the second quadrant, sine is positive, so sinθ = 4/5.
0
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Study Outcomes

  1. Understand the fundamental definitions and properties of trigonometric functions for any angle.
  2. Apply trigonometric identities and formulas to evaluate function values.
  3. Analyze the unit circle to determine reference angles and function signs.
  4. Compare different approaches for solving trigonometric equations and problems.

7.09 Quiz: Trigonometric Functions Review Cheat Sheet

  1. Master the Six Trig Functions - Ever wondered how sine, cosine, and their buddies interact? These six functions tie triangle angles to side lengths and unlock a world of wave patterns. Get comfy with sin, cos, tan, csc, sec, and cot to tackle any trig challenge! CliffsNotes
    2. CliffsNotes
  2. Get Cozy with the Unit Circle - Picture a circle of radius one centered at the origin. The unit circle helps you define trig values for all angles and explore how sine and cosine change as you spin around. It's your best friend for understanding angle behaviour across all four quadrants! Unit Circle Video
    3. Unit Circle Video
  3. Quadrant Signs Mnemonic - Use "All Students Take Calculus" to remember which trig functions are positive where. This catchy phrase tells you that in Quad I all work, in Quad II only sine, Quad III only tangent, and Quad IV only cosine shine. It's a quick hack to avoid sign slip-ups! Trigonometry Mnemonics
    4. Trigonometry Mnemonics
  4. Harness Reference Angles - Reference angles are the acute angles that your given angle makes with the x‑axis. They let you relate tricky angles back to the first quadrant, making evaluation of trig functions a breeze. Think of them as your secret shortcut to any-angle calculations! TheMathPage
    5. TheMathPage
  5. Memorize Special Angles - Lock down the sine, cosine, and tangent for 0°, 30°, 45°, 60°, and 90°. These values pop up everywhere, so knowing that sin(30°)=½ or cos(45°)=√2/2 by heart saves you precious time. It's the ultimate trig speed boost! GeeksforGeeks
    6. GeeksforGeeks
  6. Convert Degrees & Radians - Switching between degrees and radians is like speaking two languages of angle measure. Remember: degrees × (π/180) = radians and radians × (180/π) = degrees. Master this conversion and you'll seamlessly tackle problems in either world! Degree⇄Radian Guide
    7. Degree⇄Radian Guide
  7. Use Pythagorean Identities - Turn sin²θ + cos²θ = 1, 1 + tan²θ = sec²θ, and 1 + cot²θ = csc²θ into your go-to simplifiers. These identities are the superhero tools for reducing messy expressions and cracking equations. Keep them on speed dial! CliffsNotes Identities
    8. CliffsNotes Identities
  8. Remember SOH‑CAH‑TOA - This classic mnemonic means Sine = Opposite/Hypotenuse, Cosine = Adjacent/Hypotenuse, Tangent = Opposite/Adjacent. It's your trusty phrase for recalling right‑triangle ratios in a snap. Say it out loud next time you're stuck! SOH‑CAH‑TOA Guide
    9. SOH‑CAH‑TOA Guide
  9. Practice, Practice, Practice - Solve a variety of trig problems to reinforce your skills and build confidence. From evaluating functions to proving identities, every example helps you see concepts in action. The more you practice, the more intuitive trig becomes! Math You Need
    10. Math You Need
  10. Explore Coterminal Angles - Coterminal angles share the same terminal side but differ by full rotations (360° or 2π radians). They're handy for simplifying angles and finding equivalent measures. Spin around the circle mentally and watch problems get a lot easier! Coterminal Angle Demo
    11. Coterminal Angle Demo
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