Use the given function value(s), and trigonometric identities(including the cofunction identities), to find the indicated trigonometric function.
sec θ = 5
a) cos θ = 1/sec θ = 1/5
b) cot θ = cos θ/sin θ =cosθ/cos(90-θ)
I did a but im stuck for b, not sure if I'm doing it right
sin^2 + cos^2 = 1
sin = √(1 - cos^2) = √(1 - 1/25) = √(24/25) = 2√6 / 5
cot = 1/5 / (2√6 / 5) = 1 / 2√6 = √6 / 12
Draw right triangle ABC and label the sides so that secA = 5
Now you can easily see that cotA = 1/√24
To find the value of cot θ using the given value of sec θ = 5, you can use the reciprocal identity of cotangent, which states that cot θ = 1/tan θ.
First, we need to find the value of tan θ.
Since sec θ = 1/cos θ, we can rewrite sec θ as 5 = 1/cos θ.
To find cos θ, we can use the reciprocal identity of secant, which states that sec θ = 1/cos θ. In this case, we already have the value of sec θ as 5. So, we can rewrite the equation as 5 = 1/cos θ.
Now, cross-multiply the equation: 5 * cos θ = 1.
Divide both sides of the equation by 5 to isolate cos θ: cos θ = 1/5.
Now, we can substitute the value of cos θ into the equation cot θ = cos θ/sin θ.
Using the cofunction identity of sine that states sin(90 - θ) = cos θ, we can rewrite sin θ as sin(90 - θ) in terms of cos θ.
Therefore, cot θ = cos θ/sin θ = cos θ / sin(90 - θ) = cos θ / cos θ = 1.
So, the value of cot θ is 1.