Exam 1: Trigonometric Functions

Use the properties of angle measures to find the measure of each marked angle. - $a=(5 x+35)^{\circ}$ $b = ( 2 x + 92 ) ^ { \circ }$

Classify the triangle as acute, right, or obtuse and classify it as equilateral, isosceles, or scalene. -

Determine the signs of the given trigonometric functions of an angle in standard position with the given measure. -Find $\cos \theta$ , given that $\tan \theta = - \frac { 8 } { 9 }$ and $\sin \theta > 0$ .

Evaluate the expression. -Find $\cos \theta$ , given that $\tan \theta = - \frac { 4 } { 3 }$ and $\theta$ is in quadrant II.

Suppose that $\theta$ is in standard position and the given point is on the terminal side of $\theta$ . Give the exact value of the indicated trig function for $\theta$ . -(-7, 8); Find cot ϴ.

Sketch an angle in standard position such that has the least positive measure and the given point is on the terminal side of . -57°25´27´´

Use the properties of angle measures to find the measure of each marked angle. -BC

Convert the angle to decimal degrees and round to the nearest hundredth of a degree. -Find $\sin \theta$ , given that $\cos \theta = \frac { 2 } { 7 }$ and $\theta$ is in quadrant IV.

Identify the quadrant for the angle satisfying the following conditions. -Find $\csc \theta$ , given that $\sin \theta = - \frac { 2 } { 3 }$ and $\theta$ is in quadrant IV.

Place your graphing calculator in parametric and degree modes. Set the window for $T \min = 0$ , Tmax=360, Tstep=1, Xmin= -1.8, $\mathrm { Xmax } = 1.8 , \mathrm { Xscl } = 1 , \mathrm { Ymin } = - 1.2 , \mathrm { Ymax } = 1.2 , \mathrm { Yscl } = 1$ . Set the functions to $\mathrm { X } _ { 1 \mathrm {~T} } = \cos \mathrm { T } ^ { \mathrm { m } } , \mathrm { Y } _ { 1 \mathrm {~T} } = \sin \mathrm { T }$ . Graph the circle of radius 1 on the screen. Use the trace feature to move a short distance around the circle. -A wheel is rotating 240 times per minute. Through how many degrees does a point on the edge of the wheel move in $\frac { 1 } { 2 }$ seconds?

Use the fundamental identities to find the value of the trigonometric function. -sin ϴ = 7.37

Find the angle of least positive measure coterminal with the given angle. -cot ϴ, given that tan ϴ = 0.3355

Provide an appropriate response. -Find the complement of an angle whose measure is 37°10´50´´ .

The triangles are similar. Find the angle or side that corresponds to the given angle or side in the other triangle. -(-4, 0)

The triangles are similar. Find the angle or side that corresponds to the given angle or side in the other triangle. - $\text { (RS is parallel to UV.) }$

Find the exact value of the expression. -B

An equation of the terminal side of an angle in standard position is given along with a restriction on x. Find the indicated trigonometric function value of . Do not use a calculator. - $y = 3 x , x \geq 0 ; \quad$ Find $\tan \theta$

The triangles are similar. Find the missing side, angle or value of the variable. -170°

Identify the quadrant for the angle satisfying the following conditions. - $4 \tan ^ { 2 } 0 ^ { \circ } - 5 \sin ^ { 2 } 180 ^ { \circ } + 6 \csc ^ { 2 } 270 ^ { \circ }$

Perform the calculation. -Find sec ϴ, given that tan ϴ = 2.7474774 and ϴ is in quadrant I.