SOLUTION: find sec θ and tan θ if cot = 1/2 and sin θ>0

Algebra ->  Trigonometry-basics -> SOLUTION: find sec θ and tan θ if cot = 1/2 and sin θ>0      Log On


   

Question 1176335: find sec θ and tan θ if cot = 1/2 and sin θ>0
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
you are given cot%28theta%29=+1%2F2 and sin%28theta%29+%3E0+
reference angle in quadrant I where cos%28theta%29%3E+0 and sin%28theta%29+%3E0
cot%28theta%29=cos%28theta%29%2Fsin%28theta%29=1%2F2
hypotenuse of reference right triangle:

hyp=sqrt%282%5E2%2B1%5E2%29=sqrt%285%29

cos%28theta%29=1%2Fsqrt%285%29=sqrt%285%29%2F5
sin%28theta%29=2%2Fsqrt%285%29=2sqrt%285%29%2F5
and since tan%28theta%29+=1%2Fcot%28theta%29 we have
tan%28theta%29+=1%2F%281%2F2%29=2


since sec%28theta%29+=1%2Fcos%28theta%29 , we have
sec%28theta%29+=1%2F%28sqrt%285%29%2F5%29+=5%2Fsqrt%285%29=5sqrt%285%29%2F5=sqrt%285%29
and