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  • Trigonometry
  • Trigonometric identities test
  • Sum to product formulas

Sum to product formulas

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  • Question 1:
    1 pts
    		Express $\cos 2\beta -\cos 8\beta$ as a product.
    $\sin 10\beta \sin 6\beta$
    $2\sin 10\beta \sin 6\beta$
    $2\sin 5\beta \sin 3\beta$
    $\sin 5\beta \sin 3\beta$
  • Question 2:
    1 pts
    		Express $\sin 10M +\sin 4M$ as a product.

    $-2\sin 7M\cos 3M$

    $\sin 7M\cos 3M$

    $\dfrac{1}{2} \sin 7M\cos 3M$

    $2\sin 7M\cos 3M$

  • Question 3:
    1 pts
    		Express $\sin \left(\dfrac{\pi}{4}+\alpha\right)+\sin \left(\dfrac{\pi}{4}-\alpha\right)$ as a product.

    $\sqrt{2}\sin \alpha$

    $\sqrt{2}\cos \alpha$

    $\cos \alpha$

    $\sin \alpha$

  • Question 4:
    1 pts
    		$\sin(\alpha+\beta)-\sin(\alpha-\beta)=2\cos \beta \sin\alpha$
  • Question 5:
    2 pts
    		Express$\sin 20^{\circ}+\cos 50^{\circ}$ as a product.

    $\cos 40^{\circ}$

    $\cos 30^{\circ}$

    $\cos 20^{\circ}$

    $\cos 10^{\circ}$

  • Question 6:
    2 pts
    		Simplify the expression using sum to product formulas.
    $\sin 20^{\circ}+ \sin 34^{\circ}+\sin 24^{\circ}+\sin 30^{\circ}=$
  • Question 7:
    2 pts
    		Express $\cos \alpha+\cos 3\alpha+\cos 5\alpha+\cos 7\alpha$ as a product.
    $\cos\alpha \cos 2\alpha \cos 4\alpha$
    $4\cos\alpha \cos 2\alpha \cos 4\alpha$
    $4\cos\alpha \cos 6\alpha \cos 8\alpha$
    none of these
  • Question 8:
    2 pts
    		$\sin 75^{\circ}+\sin 15^{\circ}=\dfrac{\sqrt{6}}{2}$
  • Question 9:
    3 pts
    		Find the exact value of the expression.$$1+\cos x$$

    $2\cos^{2} x$

    $2\tan^{2}\left(\frac{x}{2}\right)$

    $2\sin^{2}\left(\frac{x}{2}\right)$

    $2\cos^{2}\left(\frac{x}{2}\right)$

  • Question 10:
    3 pts
    		Find the exact value of the expression.
    $$ \sec7^{\circ}(\sin 47^{\circ}+\sin 61^{\circ}-\sin 11^{\circ}-\sin25^{\circ})=$$
  • Question 11:
    3 pts
    		Find the exact value of the expression.
    $\dfrac{\cos 40^{\circ} + \cos 40^{\circ}-\cos 20^{\circ}}{\sin 20^{\circ}}=$
  • Question 12:
    3 pts
    		Express as a product. $$\tan 40^{\circ}+\cot 40^{\circ}$$
    $\dfrac{2}{\cos 20^{\circ}}$
    $\dfrac{2}{\cos 10^{\circ}}$
    $\dfrac{1}{\cos 10^{\circ}}$
    $\dfrac{2}{\sin 10^{\circ}}$

Angle Measurement

Right triangle

Unit circle

Trigonometric identities