Trigonometry Grade 11 ~ soh cah toa

Question

You know one of the basic trigonometric ratios as well as the quadrant in which the angle is located. Find the exact value of the other two basic trigonometric ratios.

a) sin A = ⅜, quadrant I

b) cos B = -¼, quadrant II

Answer 1

"ADD SUGAR TO COFFEE"

A : ALL trig functions are positive in quadrant 1

S : Sine is positive in quadrant 2

T : Tangent is positive in quadrant 3

C: Cosine is positive in quadrant 4

a) All trig functions are positive in quadrant 1

opposite = 3 and hypotenuse = 8

then by pythagorean, 8^2 = 3^2 + a^2 where a is the adjacent

64 = 9 + b^2

55 = b^2

b = sqrt(55)

then cosine is sqrt(55)/8

tangent is 3/sqrt(55) = 3*sqrt(55)/55 <-rationalizes

cosecant is 8/3

secant is 8/sqrt(55) = 8*sqrt(55)/55

cotangent is sqrt(55)/3

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b)

Only the sine is positive in quadrant 2

adjacent is -1 and hypotenuse is 4

then by pythagorean, 4^2 = (-1)^2 + b^2 where b is the opposite

16 = 1 + b^2

15 = b^2

b = sqrt(15)

the sine is sqrt(15)/4

the cosine is (given) as -1/4

the tangent is -sqrt(15)

the cosecant is 4/sqrt(15) = 4/15 * sqrt(15)

the secant is -4

the cotangent is -sqrt(15)/15