Question

NO LINKS!! Please help me​

Answer 1

Check out the attached photo

Answer 2

`\textsf{b)} \quad -(√(7))/(4)`

Explanation:

Trigonometric ratios

`\sf \sin(\theta)=(O)/(H)\quad\cos(\theta)=(A)/(H)\quad\tan(\theta)=(O)/(A)`

where:

• θ is the angle.
• O is the side opposite the angle.
• A is the side adjacent the angle.
• H is the hypotenuse (the side opposite the right angle).

`\textsf{If}\; \cos(\theta)=-(3)/(4) \implies \sf A=3 \; \textsf{and} \; H=4.`

Use Pythagoras Theorem to calculate the length of the opposite side:

`\sf \implies O^2+A^2=H^2`

`\implies \sf O=√(H^2-A^2)`

`\implies \textsf{O}=√(4^2-3^2)`

`\implies \textsf{O}=√(7)`

Therefore, substituting the values of O and H into the sine ratio:

`\implies \sin\theta=(√(7))/(4)`

As the terminal side of the angle is in Quadrant III, and sine is negative in Quadrants III and IV, the exact value of sin(θ) is:

`\implies \implies \sin\theta=-(√(7))/(4)`