Grade 11 · Math · Algebra 2

11th grade Inverse trig functions, and solving trigonometric equations worksheet

Gave an angle outside the range an inverse trig function uses (sin⁻¹ from -90° to 90°, cos⁻¹ from 0° to 180°). Shade that half of a circle together.

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

6 printable versionsChallenge Me10 questions · answer keyFree · no account

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Inverse trig functions, and solving trigonometric equations

Grade 11 Math Worksheet - Challenge Me

NameDate

Circle the best answer, or write your answer on the line.

Noah solves 4 sin²x = 3 for 0° ≤ x < 360° on a worksheet, writing answers like 10, 20. What are all the solutions?
Pia's math book asks for every x with 2 cos²x = 1 and 0° ≤ x < 360°, written like 10, 20. What are the solutions?
Ren solves 4 cos²x = 3 for 0° ≤ x < 360° on a worksheet, writing answers like 10, 20. What are all the solutions?
Tala's math book asks for every x with 3 tan²x = 9 and 0° ≤ x < 360°, written like 10, 20. What are the solutions?
Zee solves 2 sin²x − sin x = 0 for 0° ≤ x < 360° on a worksheet, writing answers like 10, 20. What are all the solutions?
Esme's math book asks for every x with 2 cos²x + cos x = 0 and 0° ≤ x < 360°, written like 10, 20. What are the solutions?
Kira's math book asks for every x with (2 cos x + √3)(sin x + 1) = 0 and 0° ≤ x < 360°, written like 10, 20. What are the solutions?
8.
Luz solves 2 sin x + √3 = 0 for 0 ≤ x < 2π on a unit circle worksheet. Which list gives every solution?
- 4π/3
- -π/3, 4π/3
- 4π/3, 5π/3
- 2π/3, 4π/3
9.
Milo's math book asks for every x with √2 cos x + 1 = 0 and 0 ≤ x < 2π. Which list gives every solution?
- 3π/4, 5π/4
- 3π/4
- π/4, 3π/4
- π/4, 7π/4
10.
Noah solves tan x + √3 = 0 for 0 ≤ x < 2π on a unit circle worksheet. Which list gives every solution?
- 2π/3
- π/3, 2π/3
- -π/3, 2π/3
- 2π/3, 5π/3

Inverse trig functions, and solving trigonometric equations. Every version has 10 questions, and the answer key prints on the second page.

I can give sin⁻¹, cos⁻¹ and tan⁻¹ of a special value, inside each inverse's range.
I can solve sin x = k or cos x = k on one turn by finding a point and its mirror.
I can solve two-step, squared and factored trig equations and list every solution.

Standard: F-TF.B.6 (+), F-TF.B.7 (+)

inverse sine (sin⁻¹): The angle from -90° to 90° with the given sine.

inverse cosine (cos⁻¹): The angle from 0° to 180° with the given cosine.

principal value: The one angle an inverse gives, inside its range.

interval: The stretch of angles allowed, like 0° ≤ x < 360°.

mirror point: The second point with the same sin (or cos), across an axis.

factor: Part of a product; a product is 0 when a factor is 0.

Gave an angle outside the range an inverse trig function uses (sin⁻¹ from -90° to 90°, cos⁻¹ from 0° to 180°). Shade that half of a circle together.

Swapped sine and cosine. Say together: the point is (cos, sin), across first, then up.

Gave the angle in degrees when radians were asked. Ask which unit the question wants, and multiply by π/180.

What is the most common mistake with inverse trig functions, and solving trigonometric equations?

Gave an angle outside the range an inverse trig function uses (sin⁻¹ from -90° to 90°, cos⁻¹ from 0° to 180°). Shade that half of a circle together.

Are these 11th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

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