Directed Angles

If $\tan \theta =-\frac{4}{3},$ then $\sin \theta$ is –

Sketch an angle of $225°$ in standard position.

Sketch an angle of $240°$ in standard position.

Sketch an angle of $270°$ in standard position.

Sketch an angle of $-135°$ in standard position.

Sketch an angle of $30°$ in standard position.

Find the smallest positive equivalent of $-40°$ by using concept of directed angles.

Find the smallest positive equivalent of $788°$ by using concept of directed angles.

_____$°$ is the sum of an exterior angle and its adjacent interior angle of a triangle.

What is the value of $\sin \left(90°+\theta \right)$?

The angle of rotation of an equilateral triangle is

The ratio of the measures of the interior angles of a regular octagon to that of a regular dodecagon is _____?

If $\left(7x+5\right)°$ and $(x+5)°$ are complementary angles, then the find value of $x$.

If the angles of a triangle are in the ratio of $1:2:3$, then find the value of the largest angle.

If one of the acute angles of a right-angled triangle is $55°$, what is the measure of the other acute angle?

The ratio of the measures of the interior angles of a regular octagon to that of a regular dodecagon is ____.

Three angles of a quadrilateral are $80°, 95°$ and $112°$, Its fourth angle is_____.

Two supplementary angles are in the ratio $3:2.$ The smaller angle measures:

Find $\cos \frac{\theta }{2}$. If $\sin \theta =-\frac{4}{5}$ and $\theta$ lies in the third quadrant.

(where $\theta \in \left[0, 2\mathrm{\pi }\right]$)

If an angle of its own complementary angle, then its measure is