SOLUTION: What is the value of sin α if tan α = -5/9 and sec α > 0?
Algebra.Com
Question 979151: What is the value of sin α if tan α = -5/9 and sec α > 0?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Since tangent is negative and secant is positive, this forces the angle to be in quadrant 4.
Draw a right triangle in this quadrant. Make the opposite leg (from the angle) 9 units long. Make the adjacent leg 5 units long. Use the pythagorean theorem to solve to get
So the sine of that angle is
Notes:
1) You can rationalize the denominator, but some books allow you to have that result. If you have to rationalize the denominator, then you should get
2) Sine is negative in Q4.
RELATED QUESTIONS
If tan α = 9 and α is acute, find the exact value of sin... (answered by tommyt3rd)
If tan α < 0 and sin α > 0, in what quadrant is α ? Explain... (answered by lwsshak3)
Using sohcahtoa: If Sin (α) = 1⁄2 what is the value of tan(α)... (answered by Fombitz,Theo)
What is the value of cos(2α) , if sin(3α) =2... (answered by MathLover1,ikleyn)
simplify... (answered by Alan3354)
Find the exact values of sin 2α, cos 2α, and tan 2α given the following... (answered by Alan3354)
Find the exact value of sin(α−β) if sin α= 12/13 and... (answered by ikleyn)
If sin α = 12/13, and cosα = 5/13, then tanα =... (answered by Alan3354)
What is the value of cos(2α) , if 2 cos(3α)=... (answered by ikleyn)