Trigonometric Identities

Fill in the blank: 1 / csc θ = ____

• sin

• cos

• tan

• cot

Answer explanation

The cosecant function, csc θ, is the reciprocal of the sine function. Therefore, 1 / csc θ equals sin θ. Thus, the correct answer is sin.

Tags

CCSS.HSF.TF.A.2

Fill in the blank: 1 / sec θ = ____

• cos

• sin

• tan

• cot

Answer explanation

1 / sec θ is the reciprocal of sec θ. Since sec θ = 1 / cos θ, it follows that 1 / sec θ = cos θ. Therefore, the correct answer is cos.

Tags

CCSS.HSF.TF.A.2

Fill in the blank: 1 / cot θ = ____

• tan

• sin

• cos

• sec

Answer explanation

1 / cot θ is equal to tan θ because cot θ is the reciprocal of tan θ. Therefore, when you take the reciprocal of cot θ, you get tan θ.

Tags

CCSS.HSF.TF.A.2

• csc

• sec

• tan

• cot

Answer explanation

The cosecant function, denoted as csc, is defined as the reciprocal of the sine function. Therefore, \( \frac{1}{\sin \theta} = \text{csc} \theta \). This makes 'csc' the correct answer.

Tags

CCSS.HSF.TF.A.2

• sec

• cosec

• tan

• cot

Answer explanation

The expression \( \frac{1}{\cos \theta} \) is the definition of the secant function, denoted as \( \sec \theta \). Therefore, the correct answer is 'sec'.

Tags

CCSS.HSF.TF.A.2

• cot

• sec

• sin

• tan

Answer explanation

The equation \( \frac{1}{\tan \theta} \) represents the cotangent function. Therefore, \( \frac{1}{\tan \theta} = \cot \theta \). The correct answer is 'cot'.

Tags

CCSS.HSF.TF.A.2

• tan

• cot

• sec

• cosec

Answer explanation

The expression \( \frac{\sin \theta}{\cos \theta} \) represents the tangent function, which is defined as the ratio of sine to cosine. Therefore, the correct answer is 'tan'.

Tags

CCSS.HSF.TF.A.2

cos θ / sin θ = _______

• cot θ

• tan θ

• sec θ

• sin θ

Answer explanation

The expression cos θ / sin θ is the definition of cotangent. Therefore, cos θ / sin θ = cot θ, making cot θ the correct answer.

Tags

CCSS.HSF.TF.A.4

sin² θ + cos² θ = _______

• 1

• 0

• 2

• sin θ

Answer explanation

The identity sin² θ + cos² θ = 1 is a fundamental trigonometric identity. It holds true for all angles θ, confirming that the correct answer is 1.

Tags

CCSS.HSF.TF.C.8

1 + tan² θ = _______

• sec² θ

• cosec² θ

• sin² θ

• cot² θ

Answer explanation

The identity 1 + tan² θ = sec² θ is a fundamental trigonometric identity. It shows the relationship between the tangent and secant functions, confirming that the correct answer is sec² θ.