05 Trigonometric Functions Free Online FlashCards

What does one radian measure?

A radian is the ratio of intercepted arc length to circle radius: $\theta=\frac{s}{r}$.

Convert $225^\circ$ to radians.

$225^\circ=\frac{5\pi}{4}$ radians.

What point corresponds to angle $t$ on the unit circle?

The terminal point is $(\cos t,\sin t)$.

State the fundamental Pythagorean identity.

The fundamental Pythagorean identity is $\sin^2 t+\cos^2 t=1$.

What are the signs of sine and cosine in Quadrant III?

In Quadrant III, both cosine and sine are negative.

When is $\tan t$ defined?

$\tan t=\frac{\sin t}{\cos t}$, so it is defined only when $\cos t\ne0$.

What is the period of $y=\sin x$?

The period of $y=\sin x$ is $2\pi$.

What is the period of $y=3\sin(2x-\frac{\pi}{2})+1$?

The period is $\frac{2\pi}{|2|}=\pi$.

State the reciprocal identity for secant.

The reciprocal identity is $\sec x=\frac{1}{\cos x}$.

State the sine addition identity.

$\sin(a+b)=\sin a\cos b+\cos a\sin b$.

Give one double-angle identity for cosine.

$\cos(2x)=\cos^2x-\sin^2x$.

What is the principal range of $\arcsin x$?

The principal range of $\arcsin x$ is $\left[-\frac{\pi}{2},\frac{\pi}{2}\right]$.