1. (P -15/17, -8/17) is found on the unit circle. Find sinΘ and cosΘ
Work:
P= (-15/17, -8/17)
cosΘ = a value
P = (a,b)
sinΘ = b value
Answer:
cosΘ = -15/17
sinΘ = -8/17
2. Should the triangle be solved beginning with Law of Sines or Law of Cosines. THen solve the triangle and found to the nearest tenth. a = 16, b = 13, c = 10.
Work:
c^2 = a^2 + b^2 -2abcosC
100-16^2+13^2-2*16*13cosC
100= 256+169 -416cosC
100=425-416cosC
-325=-416cosC
.78125=cosC
Answer: 38.6°, Law of Cosines is used
3. Should the triangle be solved beginning with Law of Sines or Law of Cosines. Then solve the triangle and round to the nearest tenth. A = 56 degrees, B = 38 degrees, a = 13.
Work:
SinA/a = SinB/b
sin56/13= sin38/b
Answer: 9.7
3. Find the exact value of tan(-3pi)
Work: tan(-3pi) = tan(-3pi+2pi) = tan (-pi) = tan (-pi+2pi) = tan (pi) = sin(pi)/cos(pi) = (0)/(-1) = 0
Answer : 0
15 years ago
9 years ago
simplify the expression tan 20 degrees +tan 25 degrees/ 1-tan 20 degrees tan 25 degrees
1 year ago
1. To find sinΘ and cosΘ for point P (-15/17, -8/17) on the unit circle, we can use the values of x and y coordinates. The x-coordinate represents the cosΘ and the y-coordinate represents the sinΘ.
For point P, the x-coordinate is -15/17, so cosΘ = -15/17.
The y-coordinate is -8/17, so sinΘ = -8/17.
Therefore, sinΘ = -8/17 and cosΘ = -15/17.
2. To solve the triangle with sides a = 16, b = 13, and c = 10, we can determine which formula to use, either Law of Sines or Law of Cosines.
Using Law of Cosines:
c^2 = a^2 + b^2 - 2abcosC
Substituting the given values:
10^2 = 16^2 + 13^2 - 2(16)(13)cosC
100 = 256 + 169 - 416cosC
-325 = -416cosC
cosC = -325/-416 = 0.78125
Now we can find the angle C using the inverse cosine function:
C = arccos(0.78125)
C ≈ 38.6°
Therefore, we used the Law of Cosines and found that angle C is approximately 38.6°.
3. To solve the triangle with angles A = 56 degrees, B = 38 degrees, and side a = 13, we can determine which formula to use, either Law of Sines or Law of Cosines.
Using Law of Sines:
SinA/a = SinB/b
Substituting the given values:
sin(56)/13 = sin(38)/b
Solving for b:
b = (13 * sin(38)) / sin(56)
b ≈ 9.7
Therefore, we used the Law of Sines and found that side b is approximately 9.7.
4. To find the exact value of tan(-3pi), we can use the periodicity property of the tangent function.
tan(-3pi) = tan(-3pi + 2pi) = tan(-pi)
Since tan is an odd function, tan(-pi) = -tan(pi)
Using the fact that sine is an odd function and cosine is an even function, we have:
-tan(pi) = -sin(pi) / cos(pi)
Since sin(pi) = 0 and cos(pi) = -1:
-tan(pi) = 0 / (-1) = 0
Therefore, the exact value of tan(-3pi) is 0.