Advertisements
Advertisements
Question
In the following, trigonometric ratios are given. Find the values of the other trigonometric ratios.
`sec theta = 13/5`
Advertisements
Solution
`sec theta = "โ๐ฆ๐๐๐ก๐๐๐ข๐ ๐"/"๐๐๐๐๐๐๐๐ก ๐ ๐๐๐" = 13/5`
Now consider a right-angled Δle ABC
By applying Pythagoras theorem
๐ด๐ถ2 = ๐ด๐ต2 + ๐ต๐ถ2
169 = ๐ฅ2 + 25
๐ฅ2 = 169 − 25 = 144
๐ฅ = 12
`cos theta = 1/sec theta = (1/13)/5 = 5/13`
`tan theta = "๐๐๐๐๐ ๐๐ก๐ ๐ ๐๐๐"/"๐๐๐๐๐๐๐๐ก ๐ ๐๐๐" = 12/5`
`sin theta = "๐๐๐๐๐ ๐๐ก๐ ๐ ๐๐๐"/"โ๐ฆ๐๐๐ก๐๐๐ข๐ ๐" = 12/13`
`cosect theta = 1/sin theta = 1/(12/13) = 13/12`
`sec theta = 1/cos theta = 1/(5/13) = 13/5`
`cot theta = 1/tan theta = 1/(12/5) = 5/12`
APPEARS IN
RELATED QUESTIONS
In Given Figure, find tan P – cot R.
If sin A = `3/4`, calculate cos A and tan A.
In the following, one of the six trigonometric ratios is given. Find the values of the other trigonometric ratios.
`tan alpha = 5/12`
In the following, one of the six trigonometric ratios is given. Find the values of the other trigonometric ratios.
`cos theta = 12/2`
if `cos theta = 3/5`, find the value of `(sin theta - 1/(tan theta))/(2 tan theta)`
if `cot theta = 3/4` prove that `sqrt((sec theta - cosec theta)/(sec theta +cosec theta)) = 1/sqrt7`
if `sin theta = 3/4` prove that `sqrt(cosec^2 theta - cot)/(sec^2 theta - 1) = sqrt7/3`
Evaluate the following
sin2 30° + sin2 45° + sin2 60° + sin2 90°
Evaluate the Following
cosec3 30° cos 60° tan3 45° sin2 90° sec2 45° cot 30°
Find the value of x in the following :
`2 sin x/2 = 1`
Find the value of x in the following :
cos 2x = cos 60° cos 30° + sin 60° sin 30°
In ΔABC is a right triangle such that ∠C = 90° ∠A = 45°, BC = 7 units find ∠B, AB and AC
If `sqrt2 sin (60° – α) = 1` then α is ______.
If sin A = `1/2`, then the value of cot A is ______.
Prove the following:
If tan A = `3/4`, then sinA cosA = `12/25`
The value of the expression (sin 80° – cos 80°) is negative.
If sin θ + cos θ = `sqrt(2)` then tan θ + cot θ = ______.
The maximum value of the expression 5cosα + 12sinα – 8 is equal to ______.
If cosec θ = `("p" + "q")/("p" - "q")` (p ≠ q ≠ 0), then `|cot(π/4 + θ/2)|` is equal to ______.
If θ is an acute angle of a right angled triangle, then which of the following equation is not true?
