SOLUTION: How do I slove for x? Also what is the correct answer?
sin(x − 20)° = cos(x)°
Algebra.Com
Question 969844: How do I slove for x? Also what is the correct answer?
sin(x − 20)° = cos(x)°
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
sin (x-20) is the sine of the difference of two angles.
sin (a-b)= sin(a)cos(b) – cos(a)sin(b)
[sin x * cos (20)] - [cos x * sin (20)] = cos x
cos 20=0.940
sin 20 =0.342
0.940* sin x - 0.342 cos x = cos x
Add 0.342 cos x to both sides
0.940 sin x=1.342 cos x
divide by 0.940
sin x= 1.428 cos x
square both sides.
sin^2 x=2.038 cos^2 x
sin ^2 x=1-cos ^2 x ; This comes from the fact that sin^2 + cos^2= 1
1-cos^2 x = 2.038 cos^2 x
1= 3.038 cos ^2 x
Divide by 3.038
0.329= cos^2 x
Take the square root:
0.574= cos x
Take the arc cos, and x=54.99 deg.
Go back to the original problem.
sin (x-20)=cos x ; This is sin (34.99)= 0.574 (or it should!). And within rounding error, it does.
RELATED QUESTIONS
By using sum or difference formulas, sin(x−pi) can be written as:?
A. -sin (x)
B. (answered by lwsshak3)
Hei!
simplify:
{{{... (answered by lwsshak3)
How do I prove that (cos^3(x)+ sin^2(x)cos(x))/(cos(x))=tan(x) is an... (answered by ikleyn)
How do I sovle the following equation?
sin(x)+cos(x)=... (answered by lwsshak3)
How. Do I slove... (answered by jim_thompson5910)
How do I evaluate these this two sine and cosine problems. Difficult!?
Evaluate cos(a... (answered by richard1234)
How do I evaluate these this two sine and cosine problems. Difficult!?
Evaluate cos(a... (answered by stanbon)
Simplify the expression:
cos(-x)/sin(-x) - cos(-x)/sin(x)
Here is my solution which I (answered by Tatiana_Stebko)