Trigonometric Ratios and Their Relationships

The video tutorial explains how to find the trigonometric ratios for an acute angle E, given the sine and cotangent values. It uses the SOH-CAH-TOA mnemonic to derive the definitions of sine, cosine, and tangent. The tutorial demonstrates how to calculate the cosine and secant of angle E, solve for the adjacent side using cotangent, and verify the results with the Pythagorean theorem.

What mnemonic is used to remember the definitions of trigonometric ratios?

• SIN-COS-TAN

• TRIG-RATIOS

• SINE-COSINE-TANGENT

• SOH-CAH-TOA

If the sine of angle E is 5 over the square root of 41, what is the cosecant of E?

• Square root of 41 over 8

• 8 over 10

• 5 over square root of 41

• Square root of 41 over 5

What is the relationship between cosine and secant?

• Secant is the inverse of sine

• Secant is the square of cosine

• Secant is the same as cosine

• Secant is the reciprocal of cosine

What is the tangent of angle E if the opposite side is 5 and the adjacent side is 'a'?

• a minus 5

• 5 times a

• a over 5

• 5 over a

How do you solve for 'a' using the given cotangent value of 8/10?

• Set a/5 equal to 10/8

• Set a/5 equal to 5/8

• Set a/5 equal to 8/10

• Set a/5 equal to 4/5

What is the simplified value of cotangent of E given as 8/10?

• 8/5

• 5/4

• 4/5

• 10/8

What is the cosine of E after solving for 'a'?

• Square root of 41 over 5

• 4 over square root of 41

• Square root of 41 over 4

• 5 over square root of 41

How can the value of 'a' be verified using the Pythagorean theorem?

• Check if 4^2 + 5^2 equals 41

• Check if 5^2 + 4^2 equals 41

• Check if 4^2 + 5^2 equals square root of 41

• Check if 5^2 + 4^2 equals square root of 41

What is the secant of E after determining 'a'?

• Square root of 41 over 4

• 4 over square root of 41

• 5 over square root of 41

• Square root of 41 over 5

What does the Pythagorean theorem confirm about the triangle?

• The sides satisfy the equation 4^2 + 5^2 = square root of 41

• The sides satisfy the equation 4^2 + 5^2 = 41

• The sides satisfy the equation 5^2 + 4^2 = 41

• The sides satisfy the equation 5^2 + 4^2 = square root of 41