The terminal side of angle \( \theta \) is in quadrant III, and the value of \( \sin \theta = - \frac { 3 } { 8 } \) . What are the exact values of \( \sin \theta , \cos \theta , \) and \( \tan \theta \) ? Work:
The value of \( x = \)
The value of \( y = \)
The value of \( r = \)
The terminal side of the angle passes through quadrant
-\(\sqrt{55}\)
-3
8
III
Lupe and Byron start riding their bikes from the same location. Lupe rides \( 24 \) miles north while Byron rides \( 7 \) miles east. How far apart are Lupe and Byron when they stop riding? HINT: draw a picture.
Use a calculator to show that each of the following pairs of coterminal angles \( \theta \) and \( \beta \) have the same values, correct to four decimals, for the sine ratio.
a. \( \theta = 100 ^ { \circ } , \beta = 460 ^ { \circ } \) b. \( \theta = 245 ^ { \circ } , \beta = - 115 ^ { \circ } \)
c. \( \theta = - 75 ^ { \circ } , \beta = - 1155 ^ { \circ } \) d. \( \theta = 2000 ^ { \circ } , \beta = 920 ^ { \circ }\)
