Advertisements
Advertisements
Question
Find the other trigonometric functions:
If cos θ = `-3/5` and 180° < θ < 270°.
Solution
Since 180° < θ < 270°, θ lies in the third quadrant.
We have cos θ = `-3/5`
Now, sin2θ + cos2θ = 1
∴ sin2θ = 1 – cos2θ = `1 - (-3/5)^2`
= `1 - 9/25`
= `16/25`
∴ sin θ = `± 4/5`
But θ lies in the third quadrant.
∴ sin θ is negative.
∴ sin θ = `-4/5`
∴ cosec θ = `1/sinθ = 1/((-4/5)) = -5/4`
sec θ = `1/cosθ = 1/((-3/5))= -5/3`
tan θ = `sinθ/cosθ = ((-(4)/5))/((-(3)/5)) = 4/3`
cot θ = `1/tanθ = 1/((4/3)) = 3/4`
APPEARS IN
RELATED QUESTIONS
State the signs of tan 380°
State the signs of cot 230°
State the signs of sec 468°
State the quadrant in which θ lies if :
cos θ < 0 and tan θ > 0
If cos θ = `12/13`, 0 < θ < `pi/2`, find the value of `(sin^2theta - cos^2theta)/(2sinthetacostheta), 1/(tan^2theta)`
Using tables evaluate the following :
4 cot 45° – sec2 60° + sin 30°
Using tables evaluate the following :
`cos^2 0 + cos^2 pi/6 + cos^2 pi/3 + cos^2 pi/2`
Find the other trigonometric functions:
If cot x = `3/4`, x lies in the third quadrant.
Find the other trigonometric functions:
If tan x = `(-5)/12`, x lies in the fourth quadrant.
If 2 sinA = 1 = `sqrt(2)` cosB and `pi/2` < A < `pi`, `(3pi)/2` < B < `2pi`, then find the value of `(tan"A" + tan"B")/(cos"A" - cos"B")`
If 2cos2θ − 11cosθ + 5 = 0 then find possible values of cosθ.
Answer the following:
State the signs of cosec 520°
Answer the following:
State the signs of cot 1899°
Answer the following:
State the signs of sin 986°
Answer the following:
State the quadrant in which θ lies if sin θ < 0 and cos θ < 0
Answer the following:
State the quadrant in which θ lies if sin θ > 0 and tan θ < 0
Answer the following:
Which is greater sin(1856°) or sin(2006°)?
Answer the following:
Which of the following is positive? sin(−310°) or sin(310°)
Answer the following:
Show that 1 − 2sinθ cosθ ≥ 0 for all θ ∈ R.
Answer the following:
Show that tan2θ + cot2θ ≥ 2 for all θ ∈ R
Answer the following:
If sec θ = `sqrt(2)` and `(3pi)/2 < theta < 2pi` then evaluate `(1 + tantheta + "cosec"theta)/(1 + cottheta - "cosec"theta)`
