1. If tan�θ = –√3 , what is the value of cot� ?
2. Find the value of 3sec2.4. (Round to the nearest tenth.)
14.if sinθ� = -4/5 and tanθ� = -4/3, what is
cot = 1/ tan
2.4 degrees or 2.4 radians ?
sin = -4/5 so in quadrant 3 or 4
tan is negative so in quadrant 4
hypotenuse = 5
opposite = 4
adjacent = 3
so cos theta = 3/5
and theta = -53.1 or -.93 radians
1. -1/√3
2. Is the 2.4 in radians?
14. The question is incomplete.
Theta is in the fourth quadrant, sin^-1 4/5 below the +x axis.
1.) 1/root 3
1. To find the value of cotθ when tanθ = -√3, we can use the relationship between cotangent and tangent. Cotangent is the reciprocal of tangent, so we can calculate cotθ by taking the reciprocal of -√3.
Reciprocal of -√3 = -1/(√3)
Therefore, the value of cotθ when tanθ = -√3 is -1/(√3).
2. To find the value of 3sec2.4, we need to understand the relationship between secant and cosine. Secant is the reciprocal of cosine, so we can calculate sec2.4 by taking the reciprocal of the cosine of 2.4.
To find the cosine of 2.4, we can use a scientific calculator or a trigonometric table. Once we have the value of cosine 2.4, we can take the reciprocal to find the value of sec2.4. Finally, we can multiply the result by 3 to find the value of 3sec2.4.
14. To find the value of θ given sinθ = -4/5 and tanθ = -4/3, we can use the relationship between sine, cosine, and tangent.
We know that sinθ = -4/5, which means the opposite side of the angle θ is -4 and the hypotenuse is 5. Using the Pythagorean theorem, we can find the adjacent side:
a² + b² = c², where a is the adjacent side, b is the opposite side, and c is the hypotenuse.
a² + (-4)² = 5²
a² + 16 = 25
a² = 25 - 16
a² = 9
a = √9
a = 3
So the adjacent side is 3.
Now, we can use the tangent relationship to find the angle θ:
tanθ = opposite/adjacent
tanθ = (-4)/3
Using inverse tangent (or arctan) on a calculator, we can find the angle whose tangent is -4/3. The result will give us the value of θ.