SOLUTION: I'm really stuck on this, any help is greatly appreciated! Find the exact values of the sine, cosine, and tangent of theta = -(7pi/12) Thanks again :)

Question 868399: I'm really stuck on this, any help is greatly appreciated!
Find the exact values of the sine, cosine, and tangent of theta = -(7pi/12)
Thanks again :)
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Find the exact values of the sine, cosine, and tangent of theta = -(7pi/12)
theta=-(7π/12)=(5π/12)=(2π/12+3π/12)=(π/6+π/4) (reference angle 5π/12 in quadrant III in which sin>0, cos>0, tan>0)
..
sin(π/6+π/4)=sin(π/6)*cos(π/4)+cos(π/6)*sin(π/4)=(1/2)*(√2/2)+(√3/2)*(√2/2)=√2/4+√6/4=(√2+√6)/4
cos(π/6+π/4)=cos(π/6)*cos(π/4)-sin(π/6)*sin(π/4)=(√3/2)*(√2/2)-(1/2)*(√2/2)=√6/4-√2/4=(√6-√2)/4
tan(π/6+π/4)=sin(π/6+π/4)/cos(π/6+π/4=(√2+√6)/(√6-√2)
..
Calculator check:
tan(-(7π/12))=tan(5π/12)≈3.732� (in quadrant III)
Exact value as calculated=(√2+√6)/(√6-√2)≈3.732�
..
sin(-(7π/12))=sin(5π/12)≈-0.9659 (in quadrant III)
Exact value as calculated=-(√2+√6)/4≈-0.9659�
..
cos(-(7π/12))=cos(5π/12)≈-0.2588� (in quadrant III)
Exact value as calculated=-(√6-√2)/4≈-0.2588�
RELATED QUESTIONS
Please help me with this problem... Find the exact values of the sine, cosine,... (answered by lwsshak3)

Use the given information to find the exact values of sine 2 theta, cosine 2... (answered by ikleyn)

Use the given information to find the exact value of each of the following. a) sin of... (answered by lwsshak3)

I'm thoroughly stuck on this trig problem: [(cosine of theta times cotangent of theta)... (answered by Alan3354,richard1234)

The problem is: Find the exact values of sine, cosine, and tangent of the angle;... (answered by richard1234)

I need to evaluate the (1) sine, (2) cosine, and/or (3) tangent of the angle without... (answered by Fombitz,Theo)

Hi All, Having difficulty with this particular problem on a task sheet, any help... (answered by Fombitz)

If cosine theta equals -5/9 and sine theta > 0, find the exact value of tan... (answered by stanbon)

Given that theta is an acute angle and sin(theta) = 17/37, find the exact value of... (answered by KMST)