Tangent Ratios (proofs and equivalences)
Interactive practice questions
By finding the ratio represented by $\sin\theta$sinθ, $\cos\theta$cosθ and $\tan\theta$tanθ in the given figure, we want to prove that $\frac{\sin\theta}{\cos\theta}=\tan\theta$sinθcosθ=tanθ.
Write down the expression for $\sin\theta$sinθ.
Write down the expression for $\cos\theta$cosθ.
Hence, form an expression for $\frac{\sin\theta}{\cos\theta}$sinθcosθ.
Write down the expression for $\tan\theta$tanθ.
Does $\frac{\sin\theta}{\cos\theta}=\tan\theta$sinθcosθ=tanθ?
Yes
No
Which of the following options correctly completes the identity?
$\tan z=\editable{}$tanz=
Given that $\sin x=\frac{4}{5}$sinx=45 and $\cos x=\frac{3}{5}$cosx=35, find $\tan x$tanx.
Use properties of the trigonometric functions to find the exact value of $\tan10^\circ-\frac{\sin10^\circ}{\cos10^\circ}$tan10°−sin10°cos10°