NZ Level 8 (NZC) Level 3 (NCEA) [In development]
Applications of reciprocal and Pythagorean identities

## Interactive practice questions

Solve the equation $2\cos^2\left(\theta\right)=2-\sin\theta$2cos2(θ)=2sinθ for $0\le\theta$0θ$<$<$2\pi$2π.

Easy
Approx 7 minutes

Solve the equation $2\sec^2\left(x\right)-3\tan x=11$2sec2(x)3tanx=11 for $0^\circ\le x\le360^\circ$0°x360°.

Round all values to the nearest degree.

Solve the equation $\tan^2\left(x\right)+9=3\sec^2\left(x\right)$tan2(x)+9=3sec2(x) for $0\le x\le2\pi$0x2π.

The intensity of light from a single source on a flat surface at some point is given by $I=k\cos^2\left(\theta\right)$I=kcos2(θ), where $k$k is a positive constant and $\theta$θ is the angle the light makes with the vertical.

### Outcomes

#### M8-6

Manipulate trigonometric expressions

#### 91575

Apply trigonometric methods in solving problems