Answer:
The answer is A
Step-by-step explanation:
Triangle DEF was rotated and dilated so that's why is looks different than triangle ABC, but it maintained the same shape that is presented in ABC and that is why A is the answer.
<span>(a) sin θ = 0.9263 θ = 67.9°, 112.1°
(b) cos θ = â’0.6909 θ = 133.7°, 226.3°
(c) tan θ = â’1.5416 θ = 123.0°, 303.0°
(d) cot θ = 1.3952 θ = 35.6°, 215.6°
(e) sec θ = 1.4293 θ = 45.6°, 225.6°
(f) csc θ = â’2.3174 θ = 205.6°, 334.4°
This is simply a matter of knowing how to use the trig identities and reflections. I am going to assume that you have access to an arctangent function (the ability to get the angle from the tangent of the angle) and that you have no other inverse trig functions available. The arctangent function is assumed to only work for positive tangents and returns a value between 0 and 90 degrees.
(a) sin θ = 0.9263 θ = 67.9°, 112.1°
The cos will be sqrt(1-0.9263^2) = 0.3768
The tan will be 0.9263/0.3768 = 2.4583
atan(2.4583) = 67.9°
Since the sin is positive, there are 2 angles, one in quadrant 1 and another in quadrant 2. The angle for quadrant 2 will be
180° - 67.9° = 112.1°
(b) cos θ = â’0.6909 θ = 133.7°, 226.3°
The cos is negative, but we'll use the positive value for the basic angle calculations.
sin = sqrt(1-0.6909^2) = 0.7230
tan = 0.7230/0.6909 = 1.0465
atan(1.0465) = 46.3°
Since the cos is negative, the angles are in quadrants II and III. The angles will be
180° - 46.3° = 133.7°
180° + 46.3° = 226.3°
(c) tan θ = â’1.5416 θ = 123.0°, 303.0°
atan(1.5416) = 57.0°
Since the tangent is negative, the angles are in quadrants II and IV.
180° - 57.0° = 123.0°
360° - 57.0° = 303.0°
(d) cot θ = 1.3952 θ = 35.6°, 215.6°
tan = 1/1.3952 = 0.7167
atan(0.7167) = 35.6°
Since the cot is positive, the angles are in quadrants I and III
180° + 35.6° = 215.6°
(e) sec θ = 1.4293 θ = 45.6°, 225.6°
cos = 1/1.4293 = 0.6996
sin = sqrt(1-0.6996^2) = 0.7145
tan = 0.7145/0.6996 = 1.0213
atan(1.0213) = 45.6°
Since the sec is positive, the angles are in quadrants I and III
180° + 45.6° = 225.6°
(f) csc θ = â’2.3174 θ = 205.6°, 334.4°
sin = 1/2.3174 = 0.4315
cos = sqrt(1-0.4315^2) = 0.9021
tan = 0.4315/0.9021 = 0.4783
atan(0.4783) = 25.6°
Since the csc is negative, the angles are in quadrants III and IV
180° + 25.6° = 205.6°
360° - 25.6° = 334.4°</span>
Answer:
x intercept - = 11/2 (5.50000 as a decimal)
y intercept - = 11/1 (11.00000 as a decimal)
Step-by-step explanation:
Because 3/6 is equal to 1/2 (one half).
If you are not able to use a calculator to find the square root of a number, and you do not know it, you can use a method called splitting factors. In this method you take out the smallest number of factors you can until a number is just a list of factors. For an example, we'll work with 144.
144 ----> take out a factor of 2.
(2)(72) -----> you can take out another 2
(2)(2)(36) ----> and another
(2)(2)(2)(18) ---> and another
(2)(2)(2)(2)(9) -----> Now we can't take a 2, but we can take a 3
(2)(2)(2)(2)(3)(3)
At this point, we have only prime numbers. Once you get to this step, you need to group them into groups of 2. You can only do this if they are the same number. So we have a group of 2s, another group of 2s and a group of 3s.
2-2, 2-2, and 3-3
For the last step, you eliminate one of each of the group and multiply them all together.
2*2*3 = 12
And the square root of 144 is 12. Many teachers will have you try to memorize all the square roots up to a certain number, but if you ever don't know, this works all the time.