IB Mathematics Applications & Interpretation Question Type 6: Applying the Golden Rule to Rewrite Values of Trigonometric Functions Exercises

Simplify the ratio $\frac{5-5{\sin }^{2}x}{5-5{\cos }^{2}x}$.

Simplify the expression $5-5{\cos }^2\left(x+\frac{\pi }{4}\right)$. [2 marks]

Express $5-5{\sin }^2(2x)$ in terms of $\cos (4x)$.

Express $\sqrt{5-5{\sin }^{2}x}$ in terms of $\cos x$, indicating any absolute values required.

Evaluate the indefinite integral $\int (5-5{\sin }^{2}x)dx$.

Solve the equation $\sqrt{5-5{\sin }^{2}x}=3$ for $x$ in $[0,2\pi )$.

Differentiate $f(x)=\sqrt{5-5{\sin }^{2}x}$ with respect to $x$.

In a right triangle, the hypotenuse has length $\sqrt{5}$ and the side opposite angle $x$ has length $\sqrt{5}\sin x$. Show that the length of the adjacent side is $\sqrt{5-5{\sin }^{2}x}$ and then simplify it.

Solve $5-5{\sin }^{2}x=\cos x$ for $x$ in $[0,2\pi )$.

Simplify the square of the sum $(\sin x+\sqrt{5-5{\sin }^{2}x}{)}^2$.

Simplify the expression $5-5{\sin }^{2}x$ using a Pythagorean identity.