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.

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Inverse trig functions, and solving trigonometric equations

Grade 11 Math Worksheet

NameDate

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

1.
Luz works out sin⁻¹(-1/2) on a unit circle worksheet. What is sin⁻¹(-1/2), in radians?
- -30°
- 11π/6
- 2π/3
- -π/6
2.
Milo's math book asks for cos⁻¹(-√3/2). What is cos⁻¹(-√3/2), in radians?
- 150°
- 7π/6
- 5π/6
- -π/3
3.
Noah works out tan⁻¹(√3) on a unit circle worksheet. What is tan⁻¹(√3), in radians?
- 60°
- 4π/3
- π/3
- -π/3
4.
Pia's math book asks for cos⁻¹(√3/2). What is cos⁻¹(√3/2), in radians?
- π/3
- π/6
- 11π/6
- 30°
Ren solves √2 sin x + 1 = 0 for 0° ≤ x < 360° on a worksheet, writing answers like 10, 20. What are all the solutions?
Zee solves √3 tan x + 1 = 0 for 0° ≤ x < 360° on a worksheet, writing answers like 10, 20. What are all the solutions?
7.
Jun solves cos x = 1/2 for 0 ≤ x < 2π on a unit circle worksheet. Which list gives every solution?
- π/3, 2π/3
- π/3
- π/3, 4π/3
- π/3, 5π/3
8.
Kira's math book asks for every x with sin x = -1/2 and 0 ≤ x < 2π. Which list gives every solution?
- 7π/6
- 5π/6, 7π/6
- 7π/6, 11π/6
- -π/6, 7π/6
9.
Luz solves tan x = -1 for 0 ≤ x < 2π on a unit circle worksheet. Which list gives every solution?
- 3π/4, 7π/4
- π/4, 3π/4
- 3π/4
- -π/4, 3π/4
10.
Milo's math book asks for every x with cos x = -√3/2 and 0 ≤ x < 2π. Which list gives every solution?
- 5π/6, 7π/6
- 5π/6
- π/6, 5π/6
- π/6, 11π/6

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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