rachelmaddie
Full Member
- Joined
- Aug 30, 2019
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Hi, I need my work checked for this please.
The expected values of the five remaining trigonometric functions of θ are:
Tangent
tan θ = 1 / cot (θ) = 1 /[-6/7] = -7/6
Secant
sec^2θ = 1 + tan^2θ = 1 + (-7/6)^2 = 1 + 49/36 = 85/36
sec θ = ± (√85)/ 6
Secant is positive in Quadrant four.
sec θ = (√85)/ 6
Cosine
cosθ = 1 / secθ = 6 / (√85 = 6
(√85) / 85
Sine
sin^2θ + cos^2θ = 1 —> sin^2θ = 1 - cos^2θ = 1
-[6(√85)/85]^2 = sin^2θ = 1 - 36*85/(85)^2 = 1- 36/85 = 49/85
sinθ = ± 7 / (√85) = ± 7 (√85) / 85
Sine is negative in Quadrant four.
sinθ = - 7 (√85)/ 85
Cosecant
cscθ = 1 / sinθ = - 85 / (7√85) = (- √85) / 7
These are the five remaining trigonometric functions:
tanθ = - 7/6
secθ = (√85)/ 6
cosθ = 6 (√85)/ 85
sinθ = - 7 (√85)/ 85
cscθ = - (√85)/ 7
The expected values of the five remaining trigonometric functions of θ are:
Tangent
tan θ = 1 / cot (θ) = 1 /[-6/7] = -7/6
Secant
sec^2θ = 1 + tan^2θ = 1 + (-7/6)^2 = 1 + 49/36 = 85/36
sec θ = ± (√85)/ 6
Secant is positive in Quadrant four.
sec θ = (√85)/ 6
Cosine
cosθ = 1 / secθ = 6 / (√85 = 6
(√85) / 85
Sine
sin^2θ + cos^2θ = 1 —> sin^2θ = 1 - cos^2θ = 1
-[6(√85)/85]^2 = sin^2θ = 1 - 36*85/(85)^2 = 1- 36/85 = 49/85
sinθ = ± 7 / (√85) = ± 7 (√85) / 85
Sine is negative in Quadrant four.
sinθ = - 7 (√85)/ 85
Cosecant
cscθ = 1 / sinθ = - 85 / (7√85) = (- √85) / 7
These are the five remaining trigonometric functions:
tanθ = - 7/6
secθ = (√85)/ 6
cosθ = 6 (√85)/ 85
sinθ = - 7 (√85)/ 85
cscθ = - (√85)/ 7