Question

NO LINKS!! Please help me with this problem.​

Answer 1

3 Answers:

• Choice A
• Choice C
• Choice E

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Step-by-step explanation:

Multiply the given radian angle measure by the fraction 180/pi to convert to degree form.

This gives

`\left((7\pi)/(4)\right)*\left((180)/(\pi)\right) = 315`

The pi terms cancel.

Therefore, 7pi/4 radians = 315 degrees.

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Use the unit circle (see below) to see that 315 degrees is in quadrant 4.

The terminal point that corresponds to this angle is
`\left((√(2))/(2),-(√(2))/(2)\right)`

This leads us to

`\cos(\theta) = (√(2))/(2)\\\\\sin(\theta) = -(√(2))/(2)\\\\`

Since any point on the unit circle is of the form
`(x,y) = (\cos(\theta),\sin(\theta))`

The ratio of those sine and cosine values leads to the tangent value.

`\tan(\theta) = (\sin(\theta))/(\cos(\theta))\\\\\tan(\theta) = \sin(\theta) / \cos(\theta)\\\\\tan(\theta) = -(√(2))/(2) / (√(2))/(2)\\\\\tan(\theta) = -(√(2))/(2) * (2)/(√(2))\\\\\tan(\theta) = -1\\\\`

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Go back to the 315 degree angle.

This angle is between 270 and 360, so it's in Q4.

The reference angle for anything in Q4 is 360-theta

So the reference angle here is 360-theta = 360-315 = 45.

Answer 2

`tan (\theta)=-1`

`sin (\theta)=-(√(2) )/(2)`

The measure of the reference angle is 45°

Step-by-step explanation:

`tan \left((7\pi )/(4) \right)=-1 \ \implies \ \textsf{true}`

`cos \left((7\pi )/(4) \right)=(√(2) )/(2) \ \implies \ \textsf{untrue}`

`sin\left((7\pi )/(4) \right)=-(√(2) )/(2) \ \implies \ \textsf{true}`

Reference Angle

convert the angle to degrees:

`\implies (7\pi )/(4) \ \textsf{rad} =(7\pi )/(4) * (180)/(\pi)=315 \textdegree`

So the angle is quadrant IV

For angles in quadrant IV: reference angle = 360° - angle

Therefore, reference angle = 360 - 315 = 45°