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  • Trigonometry
  • Trigonometric identities test
  • Double and half angle identities

Double and half angle identities

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  • Question 1:
    1 pts
    		Which expression represent double angle identity for sine function, $\sin 2u?$

    $\cos^{2}u-\sin^{2}u$

    $\sin^{2}u+\cos^{2}u$

    $-2\sin u \cos u $

    $2\sin u \cos u $

  • Question 2:
    1 pts
    		Which expression represent a half-angle identity for cosine, $\cos \dfrac{x}{2}?$
    $\cos \dfrac {x}{2}=\pm \sqrt{\dfrac{1-\cos x}{1+\cos x}}$
    $\cos \dfrac {x}{2}=\pm \sqrt{\dfrac{1+\cos x}{2}}$
  • Question 3:
    1 pts
    		$$\sin 2x=2\sin x$$
  • Question 4:
    1 pts
    		$$\tan \dfrac{x}{2}\neq \dfrac{1}{2}\tan x$$
  • Question 5:
    2 pts
    		Use a double-angle identity to find the exact value of $\sin 120^{\circ}.$

    $1$

    $\dfrac{\sqrt{3}}{3}$

    $\dfrac{1}{2}$

    $\dfrac{\sqrt{3}}{2}$

  • Question 6:
    2 pts
    		Simplify the expression. $$ \left(\cos 5+\sin 5\right)^{2}$$
    $1+\sin 10$
    $1+\cos 10$
    $1-\sin 10$
    $1-\cos 10$
  • Question 7:
    2 pts
    		If $\cos \theta=\dfrac{2\sqrt{5}}{5}$ and $0^{\circ}<\theta<90^{\circ}$ then find $\sin \dfrac{\theta}{2}.$
    $\sin \dfrac{\theta}{2}=$
  • Question 8:
    2 pts
    		If $\cot\theta=-\dfrac{24}{7}$ and $\dfrac{3\pi}{2}<\theta<2\pi$ then find $\tan \dfrac {\theta}{2}.$
    $\tan \dfrac {\theta}{2}=$
  • Question 9:
    3 pts
    		$$\sin 15^{\circ} \cos 15^{\circ}=\dfrac{1}{4}$$
  • Question 10:
    3 pts
    		$$\cot \dfrac{\pi}{8}-\tan\dfrac{\pi}{8}=1$$
  • Question 11:
    3 pts
    		Simplify the expression. $$\csc\alpha-\cot\alpha$$

    $\sin \dfrac{\alpha}{2}$

    $\tan \dfrac{\alpha}{2}$

    $\cos \dfrac{\alpha}{2}$

    $\cot \dfrac{\alpha}{2}$

Angle Measurement

Right triangle

Unit circle

Trigonometric identities