Question

PLEASE HELP! URGENT WILL GIVE BRAINLEST! PLEASE ANSWER ALL QUESTIONS!!! IF YOU DON'T I WILL REPORT.

Answer 1

$\\ \rm\Rrightarrow cos\theta=\dfrac{-\sqrt{2}}{2}$

$\\ \rm\Rrightarrow cos\theta=-\dfrac{1}{\sqrt{2}}$

$\\ \rm\Rrightarrow \theta=cos^{-1}(\dfrac{1}{\sqrt{2}}$

$\\ \rm\Rrightarrow \theta=135°,225°$

Option C

#2

• cos²Ø-1=0
• cosØ=±1
• Ø=0,180

Option C

#3

• sinØ=1
• Ø=π/2

Option A

#4

• 3tan²Ø-1=0
• tanØ=±1/√3
• Ø=30,150

Option D

#3

• 2tanØ-6=0
• tanØ=3
• Ø=1.25 ,4.39

Option A

Answer 2

Answer:

1.  b)  135°, 225°

2.  c)  0°, 180°

3.  a)  π/2

4.  b)  30°, 150°, 210°, 330°

5.  a)  1.25 radians and 4.39 radians

Step-by-step explanation:

Question 1

$\begin{aligned}\cos \theta & = -\dfrac{\sqrt{2}}{2}\\\implies \theta & = \cos^{-1}\left(-\dfrac{\sqrt{2}}{2}\right)\\\\& = 135^{\circ} \pm 360^{\circ}n, 225^{\circ} \pm 360^{\circ}\\\\& = 135^{\circ}, 225^{\circ}\quad \textsf{for}\:0^{\circ}\leq \theta < 360^{\circ}\end{aligned}$

Question 2

$\begin{aligned}\cos^2 \theta-1 & = 0\\\implies \cos^2 \theta & = 1\\\cos \theta & = \pm1\\\theta & = \cos^{-1}(\pm1)\\& = 0^{\circ} \pm 360^{\circ}n, 180^{\circ} \pm360^{\circ}n\\& = 0^{\circ}, 180^{\circ}\quad \textsf{for}\:0^{\circ}\leq \theta < 360^{\circ}\end{aligned}$

Question 3

$\begin{aligned}\sin \theta & = 1\\\implies \theta & = \sin^{-1}(1)\\\theta & = \dfrac{\pi}{2}\pm2\pi n\\\theta & = \dfrac{\pi}{2}\quad \textsf{for}\:0 \leq \theta < 2 \pi \end{aligned}$

Question 4

$\begin{aligned}3 \tan^2 \theta-1 & = 0\\\implies \tan^2 \theta & = \dfrac{1}{3}\\\tan \theta & = \pm\dfrac{1}{\sqrt{3}}\\\theta & = \tan^{-1}\left(\pm\dfrac{1}{\sqrt{3}}\right)\\& = 30^{\circ}\pm180^{\circ}n, 150^{\circ}\pm180^{\circ}n\\& = 30^{\circ}, 150^{\circ}, 210^{\circ}, 330^{\circ}\quad \textsf{for}\:0^{\circ}\leq \theta < 360^{\circ}\end{aligned}$

Question 5

$\begin{aligned}2 \tan \theta -6 & = 0\\\implies \tan \theta & = 3\\\theta & = \tan^{-1}(3)\\\theta & = 1.25\pm \pi n\\\theta & = 1.25, 4.39 \quad \textsf{for}\:0^{\circ}\leq \theta < 2 \pi \end{aligned}$