Introduction to Trigonometry
CH08 Question Bank
CBSE_CH08_QUESTION_BANK
Grade 10
Question:
If $\sin\theta=\dfrac{a}{b}$, find $\cos\theta$ and $\tan\theta$ in terms of $a$ and $b$.
Step-by-Step Solution
Key Concept: Use the Pythagorean identity to express cos θ in terms of a and b, then find tan θ.
$\cos^2\theta=1-\sin^2\theta=1-\dfrac{a^2}{b^2}=\dfrac{b^2-a^2}{b^2}$. [1.0 Mark]
$\cos\theta=\dfrac{\sqrt{b^2-a^2}}{b}$ (taking the positive root for an acute angle). [1.0 Mark]
$\tan\theta=\dfrac{\sin\theta}{\cos\theta}=\dfrac{a/b}{\sqrt{b^2-a^2}/b}=\dfrac{a}{\sqrt{b^2-a^2}}$. [1.0 Mark]
Correct Answer:
Confused by the solution? Ask the AI to explain a specific step, tell you where you went wrong, or break down the key trap in this question.