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  5. Sw5: Trigonometric Identities, Trigonometric Equations

SW5: Trigonometric Identities, Trigonometric Equations

Authored by Kiel Granada

Mathematics

10th Grade

Used 5+ times

SW5: Trigonometric Identities, Trigonometric Equations
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16 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Which of the following is equal to sin⁡(3π4−2π3)\sin\left(\frac{3\pi}{4}-\frac{2\pi}{3}\right) ?

sin⁡3π4cos⁡2π3+cos⁡3π4sin⁡2π3\sin\frac{3\pi}{4}\cos\frac{2\pi}{3}+\cos\frac{3\pi}{4}\sin\frac{2\pi}{3}

sin⁡3π4cos⁡2π3−cos⁡3π4sin⁡2π3\sin\frac{3\pi}{4}\cos\frac{2\pi}{3}-\cos\frac{3\pi}{4}\sin\frac{2\pi}{3}

cos⁡3π4cos⁡2π3+sin⁡3π4sin⁡2π3\cos\frac{3\pi}{4}\cos\frac{2\pi}{3}+\sin\frac{3\pi}{4}\sin\frac{2\pi}{3}

cos⁡3π4cos⁡2π3−sin⁡3π4sin⁡2π3 \cos\frac{3\pi}{4}\cos\frac{2\pi}{3}-\sin\frac{3\pi}{4}\sin\frac{2\pi}{3}\

2.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Which of the following is equal to cos⁡(3π4−2π3)\cos\left(\frac{3\pi}{4}-\frac{2\pi}{3}\right) ?

sin⁡3π4cos⁡2π3+cos⁡3π4sin⁡2π3\sin\frac{3\pi}{4}\cos\frac{2\pi}{3}+\cos\frac{3\pi}{4}\sin\frac{2\pi}{3}

sin⁡3π4cos⁡2π3−cos⁡3π4sin⁡2π3\sin\frac{3\pi}{4}\cos\frac{2\pi}{3}-\cos\frac{3\pi}{4}\sin\frac{2\pi}{3}

cos⁡3π4cos⁡2π3+sin⁡3π4sin⁡2π3\cos\frac{3\pi}{4}\cos\frac{2\pi}{3}+\sin\frac{3\pi}{4}\sin\frac{2\pi}{3}

cos⁡3π4cos⁡2π3−sin⁡3π4sin⁡2π3 \cos\frac{3\pi}{4}\cos\frac{2\pi}{3}-\sin\frac{3\pi}{4}\sin\frac{2\pi}{3}\

3.

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Evaluate: tan⁡π12\tan\frac{\pi}{12}

2+32+\sqrt{3}

2−32-\sqrt{3}

−2−3-2-\sqrt{3}

−2+3-2+\sqrt{3}

4.

FILL IN THE BLANKS QUESTION

2 mins • 1 pt

Given sin⁡θ = −0.6\sin\theta\ =\ -0.6 and θ∈QIII\theta\in\text{QIII} .

Find sin⁡2θ\sin2\theta .

(a)  

5.

FILL IN THE BLANKS QUESTION

2 mins • 1 pt

Given sin⁡θ = −0.6\sin\theta\ =\ -0.6 and θ∈QIII\theta\in\text{QIII} .

Find cos⁡2θ\cos2\theta .

(a)  

6.

FILL IN THE BLANKS QUESTION

2 mins • 1 pt

Given sin⁡θ = −0.6\sin\theta\ =\ -0.6 and θ∈QIII\theta\in\text{QIII} .

Find tan⁡2θ\tan2\theta .

(a)  

7.

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Find sin⁡2θ\sin2\theta given csc⁡θ =−2\csc\theta\ =-2 and cot⁡θ >0\cot\theta\ >0 .

32\frac{\sqrt{3}}{2}

−32-\frac{\sqrt{3}}{2}

34\frac{\sqrt{3}}{4}

−34-\frac{\sqrt{3}}{4}

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