Grade 11 · Math · Algebra 2

11th grade Sum and difference identities: exact values and trig equations worksheet

Your child used the wrong sign in the middle. sin(A + B) and cos(A − B) both have a plus between their two products.

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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Sum and difference identities: exact values and trig equations

Grade 11 Math Worksheet - Challenge Me

NameDate

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

On Ari's worksheet, tan A = 0.5 and tan B = 0.2. What is tan(A + B)? Round to 3 decimal places.
Bo's ramp makes an angle A with tan A = 0.75, and a second ramp adds angle B with tan B = 0.5. What is tan(A + B)?
In math club, Esme has tan A = 2 and tan B = 0.25 (both angles acute). What is tan(A + B)?
4.
Jun solves cos x cos 20° − sin x sin 20° = 0 for 0° ≤ x < 360°. What are the answers?
- 90° and 270°
- 110° and 290°
- 70° and 250°
5.
Luz solves cos x cos 30° + sin x sin 30° = √3/2 for 0° ≤ x < 360°. What are the answers?
- 0° and 60°
- 60° and 300°
- 30° and 330°
6.
Milo says sin(A + B) = sin A + sin B. Agree or disagree?
- Agree: it works for A = 0°
- Agree: the angles add, so the sines add
- Disagree: try A = B = 45°
7.
Noah says sin 90° = sin 30° + sin 60°. Agree or disagree?
- Agree: 30° + 60° = 90°
- Disagree: the sum is over 1
- Agree: both are special angles
8.
Pia says cos(A + B) = cos A cos B + sin A sin B. Agree or disagree?
- Agree: cosine copies sine's sign
- Agree: a sum gives a plus
- Disagree: it has a minus
9.
Ren finds sin 105° exactly. Which is right?
- −(√6 + √2)/4
- (√2 − √6)/4
- (√6 + √2)/4
10.
Tala finds cos 105° exactly. Which is right?
- (√6 + √2)/4
- (√6 − √2)/4
- (√2 − √6)/4

Sum and difference identities: exact values and trig equations. Every version has 10 questions, and the answer key prints on the second page.

I can use sin(A ± B) and cos(A ± B), and tan(A + B), with given values.
I can find exact values such as sin 75°, cos 15° and tan 15° from two special turns.
I can spot a sum or difference pattern in an equation and solve it on 0° to 360°.
I can show that sin(A + B) is not sin A + sin B.

Standard: F-TF.C.9 (+)

sum formula: A rule for the sine or cosine of two turns added

difference formula: The same for one turn minus another

exact value: A value written with roots, not a decimal

special turn: 30°, 45° or 60°, read from the special triangles

solve on 0° to 360°: Find every angle in one full turn

Your child used the wrong sign in the middle. sin(A + B) and cos(A − B) both have a plus between their two products.

Your child put a plus in the bottom of the tangent formula. tan(A + B) = (tan A + tan B) ÷ (1 − tan A tan B).

Your child added two sines, as if sin(A + B) were sin A + sin B. Try A = B = 45°: sin 90° = 1, but sin 45° + sin 45° ≈ 1.41.

What is the most common mistake with sum and difference identities: exact values and trig equations?

Your child used the wrong sign in the middle. sin(A + B) and cos(A − B) both have a plus between their two products.

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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