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

NameDate

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

On Ari's worksheet, cos A = 0.6, sin A = 0.8, cos B = 0.28 and sin B = 0.96. What is cos(A − B)?
Bo's robot turns A (cos A = 0.6, sin A = 0.8) and B (cos B = 0.8, sin B = 0.6). What is cos(A − B)?
In math club, Esme has cos A = 0.8, sin A = 0.6, cos B = 0.936 and sin B = 0.352. What is cos(A − B)?
4.
Kira finds cos 15° = cos(45° − 30°) exactly. Which is right?
- (√6 + √2)/4
- √3/2 − √2/2
- (√6 − √2)/4
5.
Luz finds cos 75° exactly. Which is right?
- (√6 + √2)/4
- (√2 − √6)/4
- (√6 − √2)/4
6.
Noah finds tan 75° exactly. Which is right?
- 2 + √3
- 2 − √3
- 1 + √3
7.
Pia tries tan(45° + 45°) with the formula. What happens?
- It equals 1, like tan 45°
- It equals 2, the sum of the tangents
- The bottom is 0, so no value
8.
Ren solves sin x cos 30° + cos x sin 30° = 1 for 0° ≤ x < 360°. What is x?
- 60°
- 120°
- 90°
9.
Tala solves cos x cos 10° + sin x sin 10° = 1 for 0° ≤ x < 360°. What is x?
- 0°
- 80°
- 10°
10.
Which single expression matches Zee's sin x cos 50° − cos x sin 50°?
- sin(x − 50°)
- sin(x + 50°)
- cos(x − 50°)

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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