We have already studied the basics of Trigonometry and the formulas of Trigonometry in the previous notes about Trigonometry. If you haven't read the notes, read it now
Question: If cotθ=87; then find all other trigonometric ratios.
Answer
Given that, cotθ=87
As shown in the figure below, let's assume that we have a right triangle △ABC, where m∠B=90°
Now from the formula of cotθ, that we learned in this notes, we know that:
cotθ=Opposite side to θAdjacent side to θ
Putting values in this equation and solving further,
∴cotθ∴87=ABBC=ABBC
From the equation above, let AB=8⋅x BC=7⋅x
Putting the values of AB and BC in the figure with △ABC
Now, that we have the values of AB, BC and AC we can find the values of sinθ, cosθ, tanθ, cosecθ and secθ by applying the formulas that we learnt in the basics of trigonometry
For sinθ,
sinθ=HypotenuseOpposite side to θ=ACAB=113⋅x8x=113⋅x8x∴sinθ=1138
For cosθ,
cosθ=HypotenuseAdjacent side to θ=ACBC=113⋅x7x=113⋅x7x∴cosθ=1137
For tanθ,
tanθ=cosθsinθ=cotθ1=871=78∴tanθ=78
For secθ,
secθ=cosθ1=11371=7113∴secθ=7113
For cosecθ,
cosecθ=sinθ1=11381=8113∴cosecθ=8113
If you have doubts, please leave a comment below.
Suggested Notes:
tan (A + B) = √3 and tan (A -B) = 1/√3 | Trigonometry Numerical
15 cot A = 8 | Find the value of sin A and sec A | Trigonometry Numerical
PQ = 12cm and PR = 13cm | Find tan P - cot R | Trigonometry Numerical
Trigonometry Formulas | sin θ, cos θ, tan θ, cosec θ, sec θ, cot θ | Trigonometry Basics
Suggested Notes:
tan (A + B) = √3 and tan (A -B) = 1/√3 | Trigonometry Numerical
15 cot A = 8 | Find the value of sin A and sec A | Trigonometry Numerical
PQ = 12cm and PR = 13cm | Find tan P - cot R | Trigonometry Numerical
Trigonometry Formulas | sin θ, cos θ, tan θ, cosec θ, sec θ, cot θ | Trigonometry Basics
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