Grade 11 · Math · Algebra 2

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

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Sum and difference identities: exact values and trig equations

Grade 11 Math Worksheet - Building Confidence

NameDate

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

Ari's robot turns A, with sin A = 0.6 and cos A = 0.8, then B, with cos B = 0.936 and sin B = 0.352. Find sin(A + B) to 3 decimal places.
On Bo's worksheet, sin A = 0.28, cos A = 0.96, cos B = 0.6 and sin B = 0.8. What is sin(A + B)? Round to 3 decimal places.
Esme's spinner turns A (sin A = 0.8, cos A = 0.6), then B (cos B = 0.8, sin B = 0.6). What is sin(A + B)?
4.
Using the table, which two special turns make 75° for Jun?
- 45° + 60°
- 60° + 30°
- 45° + 30°
5.
Using the table, what is sin 45° × cos 30°, Kira?
Use the picture in question 4.
- √6/2
- √6/4
- √5/4
6.
Using the table, how can Luz write 15° with two special turns?
Use the picture in question 4.
- 45° − 30°
- 30° − 15°
- 60° − 30°
7.
Which formula does Noah use for cos(A + B)?
- cos A cos B − sin A sin B
- cos A cos B + sin A sin B
- cos A + cos B
8.
In Pia's formula for cos(A − B), what sign sits between the two products?
- Plus
- Minus
- Times
9.
Using the formula, what is cos(45° + 45°), Tala?
- 0
- √2
- 1
10.
Using the formula, what is sin(60° − 30°), Zee?
- √3/2 − 1/2
- 1/2
- 0

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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