Question

Trigonometric Functions
Solve the following equations for 0<=x<=360.
cos(70-x)=0.5

Answer 1

One way to begin would be to solve the equation cos X = 0.5. This has two solutions, one in the 1st quadrant and 1 in the 4th. Can you find the two X values?

Once you have these X values, equate each to 70-x (one at a time) and solve for x. Be certain to check your answers (which are the x-values you've just found).

Answer 2

The first value is 10 but i'm not sure how to find the second value

Answer 3

what are y our two X values? X=60 (which produces x=10) is correct. What's your other X?

Answer 4

Which angle X, in the fourth quadrant, has a cosine of 0.5?

Answer 5

is it x=120?

Answer 6

120 degrees is not in the fourth quadrant; it's in the second.
Please try again. What angle X in the fourth quadrant has a cosine of 0.5?

Answer 7

is it 360

Answer 8

closer than before. However, Marc, cos 360 is 1.
cox X is 0.5; what is x?

Answer 9

x=60

Answer 10

We need to concentrate on Q4.

if you have a calculator, set it to degree mode and type in cos 300. what do you get?

Answer 11

0.5

Answer 12

right. so X in Q4 is 300. make sense?

Answer 13

yes

Answer 14

Thought I had it, but I've discovered a mistake in my own work.
However, if we let 70-x = 60, x=10 as you said.

Try this : let 70-x=300. What's (small) x?

Answer 15

If small x is negative, we must discard it, since small x must be between 0 and 360.

Answer 16

x=-230

Answer 17

That's same as mine. Because it's negative, we feed it to the dogs.

Answer 18

that leaves us with one final answer: small x = what?

Answer 19

x=10

Answer 20

right. very good.

Answer 21

Thank you @mathmale :)

Answer 22

My great pleasure! See you again.

Answer 23

cos(70-x)=0.5
70-x=cos^{-1} 0.5
70-x= 60
x=10

Answer 24

since cos, x is also in the 4th quadrant , thus x =360-10=350

Answer 25

@mathmale
it is supposed to be 130
(adding 360 to the angle wont change the value of cosine )
360-230=130
thnx @mathmale