Trig Help

[dxs]

Just want to make sure I am doing this right:

1. If cos theta = 2/3 , state all possible angles.
cos theta = 2/3
cos-1 = (-2/3) = 131.8°
since cos is positive, Quadrant 4 (because that is where cos is positive)
Q4 = 360° - 131.8° = 228.2°

2. If If tan theta = -4/3 , state all possible angles.
tan theta = -4/3
tan-1 = (4/3) = 53.1°
since tan is negative, Quadrant 4 or 2 (because that is where tan is negative)
Q4 = 360° - 53.1° = 306.9°
Q2 = 180° - 53.1° = 126.9°

 

[lev888]

Just want to make sure I am doing this right:

1. If cos theta = 2/3 , state all possible angles.
cos theta = 2/3
cos-1 = (-2/3) = 131.8°
since cos is positive, Quadrant 4 (because that is where cos is positive)
Q4 = 360° - 131.8° = 228.2°

2. If If tan theta = -4/3 , state all possible angles.
tan theta = -4/3
tan-1 = (4/3) = 53.1°
since tan is negative, Quadrant 4 or 2 (because that is where tan is negative)
Q4 = 360° - 53.1° = 306.9°
Q2 = 180 - 53.1° = 126.9°

What about the fact that these are periodic functions?

 

[dxs]

What about the fact that these are periodic functions?

Oops my bad well they were in my trig review unit and I just want to make sure I'm doing them right.

 

[Steven G]

Just want to make sure I am doing this right:

1. If cos theta = 2/3 , state all possible angles.
cos theta = 2/3
cos-1 = (-2/3) = 131.8°
since cos is positive, Quadrant 4 (because that is where cos is positive)
Q4 = 360° - 131.8° = 228.2°

2. If If tan theta = -4/3 , state all possible angles.
tan theta = -4/3
tan-1 = (4/3) = 53.1°
since tan is negative, Quadrant 4 or 2 (because that is where tan is negative)
Q4 = 360° - 53.1° = 306.9°
Q2 = 180° - 53.1° = 126.9°

What does cos-1 = (-2/3) = 131.8° mean? How does (-2/3) = 131.8°? cos -1 has no meaning even if I assume that you meant that -1 was the power. Equal signs must be valid.

If cos(A) = B then cos^-1(B) = A

Cosine is positive only in quadrant 1 and 4. 228.2° is NOT in Q1 nor Q4! So you are 0 for 2. Please find two angles, one in Q1 and one in Q4 such that cosine of these two angles is 2/3. If you need help then post back saying where you are stuck.

since tan is negative, theta must be in Quadrant 4 or 2 (because that is where tan is negative)

 

[dxs]

What does cos-1 = (-2/3) = 131.8° mean? How does (-2/3) = 131.8°? cos -1 has no meaning even if I assume that you meant that -1 was the power. Equal signs must be valid.

If cos(A) = B then cos^-1(B) = A

Cosine is positive only in quadrant 1 and 4. 228.2° is NOT in Q1 nor Q4! So you are 0 for 2. Please find two angles, one in Q1 and one in Q4 such that cosine of these two angles is 2/3. If you need help then post back saying where you are stuck.

since tan is negative, theta must be in Quadrant 4 or 2 (because that is where tan is negative)

okay for the first one,
i just did the 2/3 because I didnt know how to do fractions ontop of eachother so I did them side by side with the slash inbetwen the numbers, so I assumed that would correlate to a fraction.

 

[dxs]

What does cos-1 = (-2/3) = 131.8° mean? How does (-2/3) = 131.8°? cos -1 has no meaning even if I assume that you meant that -1 was the power. Equal signs must be valid.

If cos(A) = B then cos^-1(B) = A

Cosine is positive only in quadrant 1 and 4. 228.2° is NOT in Q1 nor Q4! So you are 0 for 2. Please find two angles, one in Q1 and one in Q4 such that cosine of these two angles is 2/3. If you need help then post back saying where you are stuck.

since tan is negative, theta must be in Quadrant 4 or 2 (because that is where tan is negative)

Adjusted properly:

Exact wording of question 1:
cosθ = 2 / 3
cosθ^-1 = (-2 / 3)
= 131.8103149°

Since cosθ is positive, I assume it lands in Quadrant 4.
Q4 = 360° - 131.8103149° = 228.1896851°

(If I am doing this wrong please point out where I can correct, but going off my notes I'm really trying)

 

[dxs]

Adjusted properly:

Exact wording of question 1: View attachment 20481
cosθ = 2 / 3
cosθ^-1 = (-2 / 3)
= 131.8103149°

Since cosθ is positive, I assume it lands in Quadrant 4.
Q4 = 360° - 131.8103149° = 228.1896851°

(If I am doing this wrong please point out where I can correct, but going off my notes I'm really trying)

NEVERMIND WE'RE ALL GOOD I GOT IT

 

[Steven G]

okay for the first one,
View attachment 20479 i just did the 2/3 because I didnt know how to do fractions ontop of eachother so I did them side by side with the slash inbetwen the numbers, so I assumed that would correlate to a fraction.

Writing / for division is fine. Writing (-2/3) = 131.8° is not fine!

 

[Steven G]

Adjusted properly:

Exact wording of question 1: View attachment 20481
cosθ = 2 / 3
cosθ^-1 = (-2 / 3)
= 131.8103149°

Since cosθ is positive, I assume it lands in Quadrant 4.
Q4 = 360° - 131.8103149° = 228.1896851°

(If I am doing this wrong please point out where I can correct, but going off my notes I'm really trying)

Again you are looking for cos^-1 θ= (-2 / 3) and saying this equals 131.8103149°. No -2/3 does not equal = 131.8103149°

You mean to write cos^-1(-2/3) = 131.8103149°. I have no idea why you are using -2/3 since cos is negative while 2/3 is positive? The problem states that cosθ = 2/3. So then θ = cos^-1(2/3) = 48.19°. 48.19° is the solution for the first quadrant. The answer for the 4th quadrant, where cosine is also positive, is 360°-48.19° = 311.81°

Again, your answer for quadrant 4 of 228.1896851° can't be correct since 228.1896851° is in quadrant 3. Quadrant 4 goes from 270° to 360°!