http://i22.tinypic.com/14l7tqu.jpg
In the picture
sine sin(α) is red,
cosine cos(α) is green,
tangent tan(α) is blue.
Which one is secant: yellow or black?
[both yellow and black have same length]
It's yellow. sec = 1/cos = 1/green (hypotenuse/adjacent; assume it's a unit circle to make it easier)
In the similar triangle that equals yellow/1
so sec = yellow/1 = yellow
They are both the same length.
They'll both be sec(α) since the circle is clearly the unit circle.
1/yellow = cosα
yellow = secα
Considering the triangle involving the black line and the part-yellow line (ie yellow until the red line), the angle opposite the part yellow = π/2 - α
So sin(π/2 - α) = part yellow / black = 1/black
cosα = 1/black
secα = black
all of those trig functions are RATIOS. So sin is red/yellow, etc. So what's the question?
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Verified answer
It's yellow. sec = 1/cos = 1/green (hypotenuse/adjacent; assume it's a unit circle to make it easier)
In the similar triangle that equals yellow/1
so sec = yellow/1 = yellow
They are both the same length.
They'll both be sec(α) since the circle is clearly the unit circle.
1/yellow = cosα
yellow = secα
Considering the triangle involving the black line and the part-yellow line (ie yellow until the red line), the angle opposite the part yellow = π/2 - α
So sin(π/2 - α) = part yellow / black = 1/black
cosα = 1/black
secα = black
all of those trig functions are RATIOS. So sin is red/yellow, etc. So what's the question?