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 versionsBuilding Confidence10 questions · answer keyFree · no account

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Inverse trig functions, and solving trigonometric equations

Grade 11 Math Worksheet - Building Confidence

NameDate

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

Jun works out sin⁻¹(1/2) on a unit circle worksheet. What is sin⁻¹(1/2), in degrees?
Kira's math book asks for cos⁻¹(-1/2). What is cos⁻¹(-1/2), in degrees?
Luz works out sin⁻¹(-√3/2) on a unit circle worksheet. What is sin⁻¹(-√3/2), in degrees?
Milo's math book asks for tan⁻¹(-√3). What is tan⁻¹(-√3), in degrees?
Noah solves sin x = 1/2 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 cos x = -1/2 and 0° ≤ x < 360°, written like 10, 20. What are the solutions?
Ren solves sin x = -√3/2 for 0° ≤ x < 360° on a worksheet, writing answers like 10, 20. What are all the solutions?
it meets the circle at two points, mirror images across the x-axis. Tala's math book asks for every x with cos x = √3/2 and 0° ≤ x < 360°, written like 10, 20. What are the solutions?
Esme's math book shows 2 cos x + 3 = 4. The first steps get cos x alone. What does cos x equal?
Jun starts solving 3 tan x + 5 = 2 on a worksheet by getting tan x alone. What does tan x equal?

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.

Every sheet you scan goes into your child’s record: dated, marked and ready for the year-end portfolio. Homeschool records