Advertisements
Advertisements
Question
Find the other trigonometric functions:
If cot x = `3/4`, x lies in the third quadrant.
Solution
We have cot x =`3/4`
∴ cosec2x = 1 + cot2x
= `1 + (3/4)^2`
= `1 + 9/16`
= `25/16`
∴ cosec x = `± 5/4`
But x lies in the third quadrant
∴ cosec x is negative
∴ cosec x= `-5/4`
∴ sin x = `1/("cosec"x) = 1/((-5/4)) = -4/5`
Now, cot x = `cosx/sinx = 3/4`
∴ cos x = `3/4 sinx = 3/4(-4/5) = -3/5`
sec x = `1/cosx = 1/((-3/5)) = -5/3`
tan x = `1/cotx =1/(3/4) = 4/3`
APPEARS IN
RELATED QUESTIONS
State the signs of tan 380°
State the signs of cot 230°
State the signs of sec 468°
State the signs of cos4c and cos4°. Which of these two functions is greater?
State the quadrant in which θ lies if :
sin 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 cos θ = `-3/5` and 180° < θ < 270°.
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 `sin"A"/3 = sin"B"/4 = 1/5` and A, B are angles in the second quadrant then prove that 4cosA + 3cosB = – 5.
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 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
