rachelmaddie
Full Member
- Joined
- Aug 30, 2019
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Hi. I need my work checked please.
Since Angle θ is in Quadrant I, all the coordinates are positive.
To find the value of cos(θ), we have sin(θ) = 84/85
We know that sin^2(θ) + cos^2(θ) = 1
Substitute,
(84/85)^2 + cos^2(θ) = 1
(7,056/7,225) + cos^2(θ) = 1
cos^2(θ) = 1 - (7,056/7,225)
cos^2(θ) = (169/7,225)
cos(θ) = (13/85)
cos(θ) = (13/85)
To find the value of tan(θ), we have tan(θ) = sin(θ)/cos(θ)
We know that sin(θ) = 84/85 and cos(θ) = (13/85)
Substitute,
tan(θ) = (84/85)/(13/85)
tan(θ) = 84/13
tan(θ) = 84/13
To find the value of cot(θ), we have cot(θ) = 1/tan(θ)
We know that tan(θ) = 84/13
Therefore, cot(θ) = 13/84
cot(θ) = 13/84
To find the value of sec(θ), we have sec(θ) = 1/cos(θ)
We know that cos(θ) = (13/85)
Therefore, sec(θ) = 85/13
sec(θ) = 85/13
To find the value of csc(θ), we have csc(θ) = 1/sin(θ)
We know that sin(θ) = 84/85
Therefore, csc(θ) = 85/84
csc(θ) = 85/84
Since Angle θ is in Quadrant I, all the coordinates are positive.
To find the value of cos(θ), we have sin(θ) = 84/85
We know that sin^2(θ) + cos^2(θ) = 1
Substitute,
(84/85)^2 + cos^2(θ) = 1
(7,056/7,225) + cos^2(θ) = 1
cos^2(θ) = 1 - (7,056/7,225)
cos^2(θ) = (169/7,225)
cos(θ) = (13/85)
cos(θ) = (13/85)
To find the value of tan(θ), we have tan(θ) = sin(θ)/cos(θ)
We know that sin(θ) = 84/85 and cos(θ) = (13/85)
Substitute,
tan(θ) = (84/85)/(13/85)
tan(θ) = 84/13
tan(θ) = 84/13
To find the value of cot(θ), we have cot(θ) = 1/tan(θ)
We know that tan(θ) = 84/13
Therefore, cot(θ) = 13/84
cot(θ) = 13/84
To find the value of sec(θ), we have sec(θ) = 1/cos(θ)
We know that cos(θ) = (13/85)
Therefore, sec(θ) = 85/13
sec(θ) = 85/13
To find the value of csc(θ), we have csc(θ) = 1/sin(θ)
We know that sin(θ) = 84/85
Therefore, csc(θ) = 85/84
csc(θ) = 85/84