Find cos q if q is an angle in standard position and the point with coordinates (3, –4) lies on the terminal side of the angle.

Mathematics

1 answer:

gayaneshka [121]2 years ago

8 0

Answer:

cos q = 3/5

Step-by-step explanation:

Standard position means the vertex (point or corner of the angle) is at (0,0) and one side of the angle is glued to the positive x-axis (facts, but not technical math terms) See image. Special triangles have all three sides nice and clean with whole number lengths, we call these Pythagorean triples. 3-4-5 is your most basic Pythagorean triple. So we don't even have to calculate the hypotenuse, see image. Now the triangle shown is easy to work with, using entry-level trig...cos = ADJ/HYP. So we get 3/5=.6 BUUuuuut, the angle q in the original problem is actually the giant angle, marked in yellow (see image) and we're in the fourth quadrant which means there's negative numbers all over the place. So just to be sure the answer is .6 and not -.6 Check your signs. One trick to remember is the ASTC markings in the quadrants. I use All Students Take Calculus, but what it means is in the first quadrant All the trig functions are positive. Only Sine (and fam) are positive in the 2nd quadrant. Tan (and fam) in the 3rd and Cos and fam in the 4th quadrant. It's a good quick check.

cos q = 3/5 OR cos q = .6

You might be interested in

Osama starts with a population of 1,000 amoebas that increases 30% in size every hour for a number of hours, h. The expression 1

Blizzard [7]

Answer: The correct option is A, itis the product of the initial population and the growth factor after h hours.

Explanation:

From the given information,

Initial population = 1000

Increasing rate or growth rate = 30% every hour.

No of population increase in every hour is,

$1000\times \frac{30}{100} =1000\times 0.3$

Total population after h hours is,

$1000(1+0.3)^h$

It is in the form of,

$P(t)=P_0(t)(1+r)^t$

Where $P_0(t)$ is the initial population, r is increasing rate, t is time and [tex(1+r)^t[/tex] is the growth factor after time t.

In the above equation 1000 is the initial population and $(1+0.3)^h$ is the growth factor after h hours. So the equation is product of of the initial population and the growth factor after h hours.

Therefore, the correct option is A, itis the product of the initial population and the growth factor after h hours.

3 0

3 years ago

Read 2 more answers

Question 11 (5 points)

mariarad [96]

Answer:

Step-by-step explanation:

Add all the possible outcomes which is 32, then seperate the number of times 5 WILL appear which is 9. Divide 9 by 32 which equals 28% and turn that into a decimal. The answer is .2 hope this helps!!

8 0

3 years ago

Help for brainliest plz

Kryger [21]

Answer:

oh uhm that is 3,4 <3

Step-by-step explanation:

3 0

2 years ago

Read 2 more answers

Helppppp..... evaluate 3^-3=

elixir [45]