Advertisements
Advertisements
Question
Find the other trigonometric functions:
If tan x = `(-5)/12`, x lies in the fourth quadrant.
Solution
Given, tan x = `-5/12`
We know that,
sec2x = 1 + tan2x
= `1 + (-5/12)^2`
= `1 + 25/144`
= `169/144`
∴ sec x = `± 13/12`
Since x lies in the 4th quadrant, sec x > 0
∴ sec x = `bb(13/12)`
cos x = `1/secx`
`= 1/(13/12)`
∴ cos x `bb(= 12/13)`
tan x = `sinx/cosx`
∴ sin x = tan x · cos x
= `-5/12 xx 12/13`
∴ sin x = `bb(-5/13)`
cosec x = `1/sinx`
= `1/((-5/13))`
= `1/sinx`
∴ cosec x = `bb(-13/5)`
cot x = `1/tanx`
= `1/((-5/12))`
∴ cot x = `bb(-12/5)`
APPEARS IN
RELATED QUESTIONS
State the signs of tan 380°
State the signs of cot 230°
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
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 cos θ = `-3/5` and 180° < θ < 270°.
Find the other trigonometric functions:
If cot x = `3/4`, x lies in the third 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 cot 1899°
Answer the following:
State the signs of sin 986°
Answer the following:
State the quadrant in which θ lies if tan θ < 0 and sec θ > 0
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 tan2θ + cot2θ ≥ 2 for all θ ∈ R
