SOLUTION: Can you please explain to me how to each of them? I get easily confused in trigonometry. 1) Calculate the length of line NO. https://byuis.brainhoney.com/Resource/46824921

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Question 1041887: Can you please explain to me how to each of them? I get easily confused in trigonometry.

1) Calculate the length of line NO.
https://byuis.brainhoney.com/Resource/46824921,0/Assets/Media/Images/GEOM043_SB-3-9.jpg

2) If tan θ = 5/4, calculate the value of cos θ.
Use this picture for #3-5: https://byuis.brainhoney.com/Resource/46824921,0/Assets/Media/Images/GEOM043_SB-3-11.jpg
3) Calculate cos θ.
4) Calculate sin θ.
5) Calculate tan θ.

6) If cos θ = (2√10) / 7, calculate the value of sin θ. (two square root 10 divided by 7)
Found 2 solutions by Aldorozos, ikleyn:
Answer by Aldorozos(172) (Show Source):
You can put this solution on YOUR website!
1) We know that sin 60 = sqrt3/2
NO/OP = sin 60 = sqrt3/2
NO/24 = sqrt3/2 = 12sqrt3
2)
Using Pythagorean theorem we can calculate the smaller side of the right angle
(12)^2 - 10^2 = 144 - 100 = 44. Therefore the smaller side is the square root of 44 = sqrt44
We know now that COS = sqrt44/12
sin = 10/12
tan = sqrt44/10
6) We know that sin^2 + cos^2 = 1. We are given the cos = (2√10) / 7
We replace cos in the equation sin^2 + cos^2 = 1 with (2√10) / 7
sin^2 + 4(10)/49 = 1
sin^2 = 1- 40/49
sin^2 = + and - sqrt 9/49
sin = + 3/7 and -3/7

Answer by ikleyn(52908) (Show Source):
You can put this solution on YOUR website!
.
2) If tan θ = 5/4, calculate the value of cos θ.
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Use this trigonometry identity: = . Then you have = = = = . Hence, = +/- .