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  • Trigonometry
  • Trigonometric identities test
  • Product to sum formulas

Product to sum formulas

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  • Question 1:
    1 pts
    		Find the correct formula and express $$\cos u\cdot \sin v $$ as a sum or difference of trigonometric functions
    $\dfrac{1}{2}[\cos (u+v)-\sin(u-v)]$
    $\dfrac{1}{2}[\sin (u+v)-\sin(u-v)]$
    $\dfrac{1}{2}[\sin (u+v)-\cos(u-v)]$
  • Question 2:
    1 pts
    		Express $\sin 3x\cdot \sin 5x$ as a sum or difference of trigonometric functions.
    $\sin 3x\cdot \sin 5x = \dfrac{1}{2}\cos 2x-\dfrac{1}{2}\cos8x$
    $\sin 3x\cdot \sin 5x = \dfrac{1}{2}\sin 2x-\dfrac{1}{2}\cos8x$
    $\sin 3x\cdot \sin 5x = \dfrac{1}{2}\sin 2x-\dfrac{1}{2}\sin8x$
  • Question 3:
    1 pts
    		Express $\sin(\alpha-\beta)\cdot \cos(\alpha+\beta)$ as a sum or difference of trigonometric functions.

    $\dfrac{1}{2}\cos 2\alpha+\dfrac{1}{2}\cos 2\beta$

    $\dfrac{1}{2}\cos 2\alpha-\dfrac{1}{2}\sin 2\beta$

    $\dfrac{1}{2}\sin 2\alpha+\dfrac{1}{2}\sin 2\beta$

    $\dfrac{1}{2}\sin 2\alpha-\dfrac{1}{2}\sin 2\beta$

  • Question 4:
    2 pts
    		$$\sin(60^{\circ}-\alpha)\cdot \sin(60^{\circ}+\alpha)=\dfrac{1}{4}\left(2\cos2\alpha+1\right)$$
  • Question 5:
    2 pts
    		Find the exact value of the expression.
    $\tan 20^{\circ}\cdot \tan 40^{\circ} \cdot \tan 80^{\circ}=$
  • Question 6:
    2 pts
    		Express $4\sin\left(1+\dfrac{\pi}{6}\right)\cos\left(1+\dfrac{\pi}{3}\right)$ as a sum or difference of trigonometric functions.
    $\cos 2-1$
    $2\cos 2-1$
    $2\cos 2+1$
    $\cos 2+1$
  • Question 7:
    2 pts
    		Express $\cos \dfrac{x}{2}\cos \dfrac{y}{2}\cos \dfrac{x+y}{2}$ as a sum or difference of trigonometric functions.
    $\dfrac{1}{4}+\dfrac{1}{4}\cos x+\dfrac{1}{4} \cos y+ \dfrac{1}{4}\cos (x+y)$
    $\dfrac{1}{4}\cos x+\dfrac{1}{4} \cos y+ \dfrac{1}{4}\cos (x+y)$
    $\dfrac{1}{4}+\dfrac{1}{4}\cos x+\dfrac{1}{4} \cos y$
    $\dfrac{1}{4}+ \dfrac{1}{4}\cos (x+y)$
  • Question 8:
    3 pts
    		Simplify the expression using product to sum formulas.
    $\sin20^{\circ}\sin 40^{\circ}\sin 60^{\circ}\sin 80^{\circ}=$
  • Question 9:
    3 pts
    		$N$ is an integer in the range $[0,180]$ such that $$2\cos43^{\circ}\cos26^{\circ}= \cos69^{\circ}+\cos N.$$ What is the value of $N$?
    $\cos 20^{\circ}$
    $\cos 17^{\circ}$
    $\cos 27^{\circ}$
  • Question 10:
    3 pts
    		Express $4\sin \alpha \sin 2\alpha \sin 4\alpha$ as a sum or difference of trigonometric functions.

    $\sin 2\alpha+\sin 4\alpha+\sin 6\alpha$

    $\sin 2\alpha+\sin 4\alpha-\sin 6\alpha$

    $\sin 2\alpha-\sin 4\alpha-\sin 6\alpha$

    $\sin 3\alpha-\sin 6\alpha-\sin 9\alpha$

Angle Measurement

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Trigonometric identities