Could someone please help me with the following q's I'm having some trouble:
1.) cot θ (theta) = 0.791, find sec θ and tan θ
2.) tan θ = 9/40, what is the value sin^2θ + cos^2θ
Do you not have a calculator?
if cotØ = .791
then tanØ = 1/.791 = appr 1.264
Ø = 51.656°
secØ = 1/cosØ = 1.612
2. sin^2 Ø + cos^2 Ø = 1 , one of the major trig identities, which you MUST know.
if13 cos=12,find the value of sec a+sina?
Sure! I can help you with these questions.
1.) To find sec θ and tan θ when cot θ = 0.791, we can use the relationships between trigonometric functions.
We know that cot θ is the reciprocal of tan θ: cot θ = 1/tan θ.
So, if cot θ = 0.791, we can find tan θ by taking the reciprocal:
tan θ = 1 / cot θ = 1 / 0.791 = 1.265.
To find sec θ, we can use the relationship between sec θ and cos θ: sec θ = 1 / cos θ.
We know that cot θ = cos θ / sin θ. By substituting cot θ = 0.791, we get:
0.791 = cos θ / sin θ
Now, we can use the Pythagorean identity sin^2 θ + cos^2 θ = 1. Rearranging the equation:
cos θ = 0.791 sin θ
Substituting the value of cos θ in sec θ = 1 / cos θ:
sec θ = 1 / (0.791 sin θ)
2.) To find the value of sin^2 θ + cos^2 θ when tan θ = 9/40, we can use the Pythagorean identity sin^2 θ + cos^2 θ = 1.
We know that tan θ = sin θ / cos θ. By substituting tan θ = 9/40, we have:
9/40 = sin θ / cos θ
To solve for sin θ, we can multiply both sides by cos θ:
9 = 40 sin θ
Now we can square both sides to eliminate sin θ:
81 = 1600 sin^2 θ
Using the Pythagorean identity, we know that sin^2 θ + cos^2 θ = 1. Therefore:
sin^2 θ = 1 - cos^2 θ
Substituting this into our equation:
81 = 1600(1 - cos^2 θ)
Simplifying,
81 = 1600 - 1600cos^2 θ
Rearranging the equation,
1600cos^2 θ = 1519
Finally, dividing both sides by 1600,
cos^2 θ = 1519/1600
To find sin^2 θ + cos^2 θ, we can add sin^2 θ and cos^2 θ together:
sin^2 θ + cos^2 θ = 1.