Answered: Compute the sine, cosine, and tangent…

Mathematics For Machine Technology

8th Edition

ISBN:9781337798310

Author:Peterson, John.

Publisher:Peterson, John.

Chapter73: Achievement Review—section Seven

Section: Chapter Questions

Problem 46AR

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Question

Compute the sine, cosine, and tangent of 300° by using the reference angle.

(Type sqrt(2) for √2 and sqrt(3) for √3.)

What is the reference angle? degrees.

In what quadrant is this angle? (answer 1, 2, 3, or 4)

sin(300°)=

cos(300°)=

tan(300°)=

Expert Solution

Step 1

$R e f e r e n c e a n g l e s - R e f e r e n c e a n g l e s a r e t h o s e a n g l e s w i t h t h e h e l p o f w h i c h w e c a n m o v e i n f o u r q u a d r a n t s . W i t h t h e h e l p o f r e f r e n c e a n g l e w e c a n f i n d t h e v a l u e o f a n y a n g l e i n s i m p l e r w a y i n a n y q u a d r a n t . F o r e x a m p l e, w e k n o w t h e v a l u e s o f t r i g o n o m e t r i c r a t i o s f o r 0 °, 30 °, 45 °, 60 ° a n d 90 ° . S o i n c a s e o f a n g l e o t h e r t h a n t h e s e f i v e, w e h a v e t o u s e r e f e r e n c e a n g l e . R e f e r e n c e a n g l e s d e f i n e t h e b o u n d a r i e s o f t h e q u a d r a n t . R e f e r e n c e a n g l e s a r e - 90 °, 180 °, 270 °, 360 ° .$

Step 2

$I^{s t q u a d r a n t} - a n g l e s l i e s b e t w e e n 0 ° a n d 90 ° (0 < θ < 90) . 2^{n d q u a d r a n t} - a n g l e l i e s b e t w e e n 90 ° a n d 180 ° (90 < θ < 180) . 3^{r d q u a d r a n t} - a n g l e l i e s b e t w e e n 180 ° a n d 270 ° (180 < θ < 270) . 4^{t h q u a d r a n t} - a n g l e l i e s b e t w e e n 270 ° a n d 360 ° (270 < θ < 360) . T h e a n g l e g i v e n t o u s i s 300 ° . H e n c e t h i s a n g l e l i e s i n 4^{t h} q u a d r a n t .$

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