An acute angle θ is in a right triangle with cos θ = two thirds. what is the value of sec θ?

 the required value is

Step-by-step explanation:  Given that an acute angle θ is in a right triangle with cos θ = two thirds.

We are to find the value of sec θ.

In a right-angled triangle, we have the following relation between the cos and sec of an acute angle θ :

From the given information, we have

Therefore, we get

Thus, the required value is

d

step-by-step explanation:

hello and welcome!

so, when we see the words "proportional" along with a table, we need to know that we're looking numbers that divide by the same thing.

looking at this table, we simply have to do a trial and error, and divide to see which numbers have the same quotient. if you look at choice a & c, they both have equal quotients for three of the numbers, with one exception, so those can't be the answer. looking at b, there is no similarity, so that can't be it. then, we see d; if you divide all the numbers in the table, you'll see that they all divide by two, which is a proportional relationship, and our answer!

also, always remember that the x will always be the number that goes into y, and somewhere behind this table, is a formula. for this specific table, the formula would be:

since our x-value is being divided by two to get the y-value. and if they were to ask for more numbers in the series, this is the formula you would use to find them.

a reflection across the x-axis , followed by the by a reflection across the y-axis , and then a scale dilation of 0.5 .