If cos θ = -2/7 and tan θ <0

Question

sin

tan

cot

sec 7/-2

scs

is what i got so far

Answer 1

Lord

Well as the cosine and tangent both < 0, angle must be in 2nd quadrant.

cos = -2/7. So the line from the origin to the point must pass through (0,0) and x = -2.

The length of the line from the origin to the point must be 7.

So the distance from the x axis to the point must be sqrt (7*7 - 2*2) = √45 = √9.5 = 3√5 (simplified).

Now we can find the values you require.

sin = (3√5) / 7

tan = - (3√5) / 2

cot = -2 / (3√5)

sec -7/2 (which you got correctly)

cosec = 1 / sin = 7 / (3√5)

Mike

Answer 2

θ in quadrant II. So, sinθ = √(1 - (- 2/7)²) = 3√5/7; tanθ = sinθ/cosθ = - 3√5/2; cotθ = - 2/(3√5); secθ = 1/cosθ = - 7/2; cscθ = 1/sinθ = 7/(3√5)