# Trigonometric Relations/Identities help

• Jul 19th 2008, 05:47 AM
BG5965
Trigonometric Relations/Identities help

1a) If tan(A) = 3/4, show that sin(A) = 3/4cos(A)

1b) Therefore, evaluate:
[4sin(A) - cos(A)] / [8sin(A) + 5cos(A)]

2) Solve without a calculator, show working
a) sin(60) x tan(45)
b) 9tan^2(30)
c) 6cos(60) x sin(30)

3) If sin^2(x) = 7/8, find cos^2(x)

4) If cos^2(x) = 0.36, fins sin^2(x)

5) Find tan x if cos x = 8/17 and sin x = 15/17

6) ACD is a right angled triangle, where B is a point on AC, angle CAD = 30 deg, angle CBD = 60 deg and AB = 10.

a) By considering angle BCD, prove CD = $\displaystyle SQRT 3$ BC
b) By considering angle ACD, prove CD = [10 + BC] / [SQRT 3]
c) Use these two results to find BC

• Jul 19th 2008, 06:09 AM
Moo
Hello,

Quote:

Originally Posted by BG5965

1a) If tan(A) = 3/4, show that sin(A) = 3/4cos(A)

Use the definition of tan :

$\displaystyle \tan(A)=\frac{\sin(A)}{\cos(A)}$

Quote:

1b) Therefore, evaluate:
[4sin(A) - cos(A)] / [8sin(A) + 5cos(A)]
Substitute $\displaystyle \sin(A)=\frac 34 \cos(A)$

For example, $\displaystyle 4 \sin(A)-\cos(A)=3 \cos(A)-\cos(A)=2 \cos(A)$

Quote:

2) Solve without a calculator, show working
a) sin(60) x tan(45)
b) 9tan^2(30)
c) 6cos(60) x sin(30)
Use this unit circle : http://dcr.csusb.edu/LearningCenter/...UnitCircle.gif

Quote:

3) If sin^2(x) = 7/8, find cos^2(x)

4) If cos^2(x) = 0.36, fins sin^2(x)
Use identity $\displaystyle \cos^2(x)+\sin^2(x)=1$

Quote:

5) Find tan x if cos x = 8/17 and sin x = 15/17
Use the definition of tan I gave you above

Quote:

6) ACD is a right angled triangle, where B is a point on AC, angle CAD = 30 deg, angle CBD = 60 deg and AB = 10.

a) By considering angle BCD, prove CD = $\displaystyle SQRT 3$ BC
b) By considering angle ACD, prove CD = [10 + BC] / [SQRT 3]
c) Use these two results to find BC
Draw a sketch and use definitions of cosine, sine and tangent :

sin=opposit side/hypotenuse

If you don't know it, search on wikipedia (Wink)
• Jul 19th 2008, 07:03 AM
tutor
Hi,

2.)

sin60*tan45

=(sqrt3)/2 * 1

=(sqrt3)/2

b.)

=9tan^2(30)

=9(1/sqrt3)^2
=9(1/3)
=3

c.)

=6Cos60sin30
=6(1/2)(1/2)
=3/2

(Hi)