Find the best solutions to your problems with the help of IDNLearn.com's experts. Get step-by-step guidance for all your technical questions from our dedicated community members.
Sagot :
I did this test b4, yours is answer #number 12
Convert things to their basic forms.
Remember a few identities
sin^2 + cos^2 = 1 so
sin^2 = 1 - cos^2 and
cos^2 = 1 - sin^2
I'm going to skip typing the theta symbol, just to make things faster. Just assume it is there and fill it in as you work the problems.
Follow along to see how each problem was worked out. You'll catch on to the general technique.
======
1. sec θ sin θ
1/cos * sin = sin/cos = tan
2. cos θ tan θ
cos * sin/cos = sin
3. tan^2 θ- sec^2 θ
sin^2 / cos^2 - 1/cos^2
(sin^2 - 1)/cos^2
-(1-sin^2)/cos^2
-cos^2/cos^2
-1
4. 1- cos^2θ
sin^2
5. (1-cosθ)(1+cosθ)
Remember (a+b)(a--b) = a^2 - b^2
1-cos^2 = sin^2
6. (secx-1) (secx+1)
sec^2 -1
1/cos^2 - 1
1/cos^2 - cos^2/cos^2
(1-cos^2)/cos^2
sin^2/cos62
tan^2
7. (1/sin^2A)-(1/tan^2A)
1/sin^2 - 1/(sin^2/cos^2)
1/sin^2 - cos^2/sin^2
(1-cos^2)/sin^2
sin^2/sin^2
1
8. 1- (sin^2θ/tan^2θ)
1-sin^2/(sin^2/cos^2)
1 - sin^2*cos^2/sin^2
1-cos^2
sin^2
9. (1/cos^2θ)-(1/cot^2θ)
1/cos^2 - 1/(cos^2/sin^2)
1/cos^2 - sin^2/cos^2
(1-sin^2)/cos^2
cos^2/cos^2
1
10. cosθ (secθ-cosθ)
cos *(1/cos - cos)
1-cos^2
sin^2
11. cos^2A (sec^2A-1)
cos^2 * (1/cos^2 - 1)
1 - cos^2
sin^2
12. (1-cosx)(1+secx)(cosx)
(1-cos)(1+1/cos)cos
(1-cos)(cos + 1)
-(cos-1)(cos+1)
-(cos^2 - 1)
-(-sin^2)
sin^2
13. (sinxcosx)/(1-cos^2x)
sin*cos/sin^2
cos/sin
cot
14. (tan^2θ/secθ+1) +1
(sin^2/cos^2)/(1/cos) + 2
sin^2/cos + 2
sin*tan + 2
Convert things to their basic forms.
Remember a few identities
sin^2 + cos^2 = 1 so
sin^2 = 1 - cos^2 and
cos^2 = 1 - sin^2
I'm going to skip typing the theta symbol, just to make things faster. Just assume it is there and fill it in as you work the problems.
Follow along to see how each problem was worked out. You'll catch on to the general technique.
======
1. sec θ sin θ
1/cos * sin = sin/cos = tan
2. cos θ tan θ
cos * sin/cos = sin
3. tan^2 θ- sec^2 θ
sin^2 / cos^2 - 1/cos^2
(sin^2 - 1)/cos^2
-(1-sin^2)/cos^2
-cos^2/cos^2
-1
4. 1- cos^2θ
sin^2
5. (1-cosθ)(1+cosθ)
Remember (a+b)(a--b) = a^2 - b^2
1-cos^2 = sin^2
6. (secx-1) (secx+1)
sec^2 -1
1/cos^2 - 1
1/cos^2 - cos^2/cos^2
(1-cos^2)/cos^2
sin^2/cos62
tan^2
7. (1/sin^2A)-(1/tan^2A)
1/sin^2 - 1/(sin^2/cos^2)
1/sin^2 - cos^2/sin^2
(1-cos^2)/sin^2
sin^2/sin^2
1
8. 1- (sin^2θ/tan^2θ)
1-sin^2/(sin^2/cos^2)
1 - sin^2*cos^2/sin^2
1-cos^2
sin^2
9. (1/cos^2θ)-(1/cot^2θ)
1/cos^2 - 1/(cos^2/sin^2)
1/cos^2 - sin^2/cos^2
(1-sin^2)/cos^2
cos^2/cos^2
1
10. cosθ (secθ-cosθ)
cos *(1/cos - cos)
1-cos^2
sin^2
11. cos^2A (sec^2A-1)
cos^2 * (1/cos^2 - 1)
1 - cos^2
sin^2
12. (1-cosx)(1+secx)(cosx)
(1-cos)(1+1/cos)cos
(1-cos)(cos + 1)
-(cos-1)(cos+1)
-(cos^2 - 1)
-(-sin^2)
sin^2
13. (sinxcosx)/(1-cos^2x)
sin*cos/sin^2
cos/sin
cot
14. (tan^2θ/secθ+1) +1
(sin^2/cos^2)/(1/cos) + 2
sin^2/cos + 2
sin*tan + 2
Your participation is crucial to us. Keep sharing your knowledge and experiences. Let's create a learning environment that is both enjoyable and beneficial. For dependable answers, trust IDNLearn.com. Thank you for visiting, and we look forward to helping you again soon.