cotA = tan(90degrees- A) True or False
The vectors <4, 5> and <-10, 8> are orthogonal True or False
2<3, 5> = 16 True or False
<2. 3>*<4, 3> =
<2, 6> + <4, 5> =
Find c if a = 3, b = 5, and A = 30degrees=
the co- in the trig functions means co-mplementary angle.
cos(x) = sin(90-x)
cot(x) = tan(90-x)
csc(x) = sec(90-x)
#2 true. review the dot product.
#3 eh? a vector and a scalar?
#4 2*4 + 3*3
if * means dot product
#5 <2+4,6+5>
for the last one, use the law of sines to find B:
sinB/5 = sin30/3
Now, with B, C=180-(A+B) and using the law of cosines,
c^2 = 3^2+5^2-2*3*5cosC
To determine the veracity of the given statements, let's break down each question and explain how to find the answer.
1. cotA = tan(90 - A) (True or False):
To evaluate this statement, use the trigonometric identities. The cotangent of an angle is equal to the tangent of the complementary angle. So, cotA = tan(90 - A) is true.
2. The vectors <4, 5> and <-10, 8> are orthogonal (True or False):
Two vectors are orthogonal if their dot product is zero. To check if these vectors are orthogonal, calculate their dot product. The dot product of two vectors <a, b> and <c, d> is ac + bd. So, for the given vectors, the dot product is (4 * -10) + (5 * 8) = -40 + 40 = 0. Therefore, the vectors <4, 5> and <-10, 8> are orthogonal. Hence, the statement is true.
3. 2<3, 5> = 16 (True or False):
In this statement, you are multiplying a vector <3, 5> by a scalar value of 2. Multiplying a vector by a scalar involves multiplying each component of the vector by the scalar. So, 2<3, 5> = <6, 10>. Comparing this to 16, we see that <6, 10> is not equal to 16. Therefore, the statement is false.
4. <2, 3> * <4, 3> =
To calculate the dot product of two vectors, multiply the corresponding components and sum the results. For the given vectors, <2, 3> and <4, 3>, the dot product is (2 * 4) + (3 * 3) = 8 + 9 = 17. Therefore, <2, 3> * <4, 3> = 17.
5. <2, 6> + <4, 5> =
To add two vectors, add their corresponding components. For the given vectors, <2, 6> and <4, 5>, the sum is (2 + 4, 6 + 5) = <6, 11>. Therefore, <2, 6> + <4, 5> = <6, 11>.
6. Find c if a = 3, b = 5, and A = 30 degrees:
To find the unknown side in a triangle using the Law of Sines, the formula is a/sin(A) = c/sin(C), where a and A are given sides and angles, and c and C are the unknown side and angle, respectively. Plugging in the given values, we have 3/sin(30) = c/sin(C). Rearrange the equation to solve for c: c = (3 * sin(C)) / sin(30). Then, use a calculator to evaluate sin(C) and sin(30) to find the value of c.
Remember that it's essential to understand the underlying concepts and formulas to solve these questions, but substituting the given values into the equations correctly is equally important.