1. If tan�θ = –√3 , what is the value of cot� ?
2. Find the value of 3sec2.4. (Round to the nearest tenth.)
7. if �θ is a standard position angle and cotθ� = 1.85, in which quadrant(s) could θ� lie?
14.if sinθ� = -4/5 and tanθ� = -4/3, what is the value of cosθ� ?
19. if tanθ� = √33/4, use the fundamental identities to find sin�θ < 0
please help me
1. cot = 1/tan
2. sec = 1/cos
7. tan,cot > 0 in QI,QIII
14. cos = sin/tan
19. 4^2 + (√17)^2 = (√33)^2, sin = tan*cos
so, what are your answers?
oops
19. 4^2 + (√33)^2 = (√49)^2
1. To find the value of cotθ, we can use the reciprocal relationship between tangent (tan) and cotangent (cot). The equation "tanθ = –√3" tells us that the tangent of angle θ is equal to –√3.
The reciprocal relationship states that cotθ is equal to 1 divided by tanθ. So, to find cotθ, we can compute 1 divided by –√3.
Answer: cotθ = −1/√3, or −√3/3.
2. To find the value of 3sec2.4, we need to evaluate the secant (sec) function for the angle 2.4.
Secant is the reciprocal of cosine (cos). Since the question doesn't provide the value of cos2.4 directly, we need to find it first.
To find cos2.4, we can use the identity: sec^2θ = 1 + tan^2θ. Rearranging the equation gives us: cos^2θ = 1/ sec^2θ.
Next, we can substitute 2.4 into this equation. So, cos^2(2.4) = 1/ sec^2(2.4).
Now, find cos(2.4) by taking the square root of both sides: cos(2.4) = ±sqrt(1/ sec^2(2.4)).
Since we are looking for the nearest tenth, we evaluate the expression using a calculator and round to the nearest tenth.
Answer: The value of 3sec2.4 is approximately 3.6.
7. The cotangent (cot) of an angle θ is equal to 1 divided by the tangent (tan) of θ. The equation "cotθ = 1.85" tells us the cotangent is 1.85.
Since cotθ is positive (given by the equation), we know that θ lies in either the first or third quadrant. However, we cannot determine the specific quadrant based on cotθ alone. We need more information to determine the quadrant accurately.
14. To find the value of cosθ, we can use the given information in the problem. We know sinθ = -4/5 and tanθ = -4/3.
Using the pythagorean identity sin²θ + cos²θ = 1, we can substitute the given value of sinθ and solve for cosθ.
(-4/5)² + cos²θ = 1
16/25 + cos²θ = 1
cos²θ = 1 - 16/25
cos²θ = 9/25
Next, find the square root of both sides to find the value of cosθ.
cosθ = ±sqrt(9/25)
Since it's not mentioned if θ is in the positive or negative direction, cosθ could be positive or negative. However, we are not given enough information to determine the exact value of cosθ.
19. To determine whether sinθ < 0, we need to use the given information that tanθ = √33/4.
We can use the identity tanθ = sinθ / cosθ.
Given that tanθ = √33/4, we can rewrite it as sinθ / cosθ = √33/4.
Next, square both sides of the equation:
(sinθ / cosθ)^2 = (√33/4)^2
(sinθ)^2 / (cosθ)^2 = (33/16)
Using the Pythagorean identity sin^2θ + cos^2θ = 1, we substitute (cosθ)^2 with (1 - sin^2θ):
(sinθ)^2 / (1 - sin^2θ) = (33/16)
Now, we can rearrange the equation:
(16 * sin^2θ) / (1 - sin^2θ) = 33
Simplifying the equation yields:
16sin^2θ = 33 - 33sin^2θ
49sin^2θ = 33
sin^2θ = 33/49
sinθ = ±√(33/49)
sinθ = ±(√33/7)
Since sinθ is negative in the third and fourth quadrants, we can conclude:
Answer: sinθ < 0 in the third and fourth quadrants.