Trigonometry PRACTICE Test

Online Homework System Assignment Worksheet

6/21/18 - 3:44 PM

Name: ____________________________ Class: American Public University System - Precalculus (MATH111 C003 Win 18) (3u7gt5)

Class #: ____________________________ Section #: ____________________________ Instructor:Maple T.A. Administrator Assignment:PRACTICE TEST 7.4

Question 1: (1 point)

Decompose into the sum of two orthogonal vectors and where

and

__________ , __________

__________ ,__________

Question 2: (1 point)

Find the projection of onto

__________ __________

Question 3: (1 point)

Identify which pair of vectors is parallel, which pair is orthogonal, and which is neither.

(a) and . __________

(b) and . __________

w⇀ w1 ⇀ w2

⇀ = .w1 ⇀ proj

z⇀ w⇀

= ⟨2, −12⟩w⇀ = ⟨−3, 4⟩z⇀

=w1 ⇀ ⟨ ⟩

=w2 ⇀ ⟨ ⟩

= ⟨2 , −5⟩w⇀ = ⟨− , ⟩ .z⇀ 16 37 =proj

z⇀ w⇀ ⟨ ⟩

= ⟨ , − ⟩u⇀ 13 13 = ⟨− 2, − 2⟩v⇀

= 4 − 4w⇀ i ⇀

j ⇀

= − 12 +12x⇀ i ⇀

j ⇀

= ⟨− , ⟩⇀ 3 3 = ⟨4, − 1⟩⇀

(c) and . __________

Question 4: (1 point)

Find the angle between and .

Round to the nearest tenth.

____________ °

Question 5: (1 point)

Find the angle between and . Round to the nearest tenth.

____________ °

Question 6: (1 point)

Find the angle between and .

__________

Question 7: (1 point)

Find the magnitude of the vector given in the equation.

= ⟨− , ⟩y⇀ 35 34 = ⟨4, − 1⟩z⇀

θ = 3.4 +3.8z⇀ i ⇀

j ⇀

= 0.5 +4.6u⇀ i ⇀

j ⇀

θ ≈

θ = ⟨− 1.8, 5.5⟩z⇀ = ⟨1, − 4.6⟩u⇀

θ ≈

θ = cos + sinz⇀ 3π4 i ⇀ 3π

4 j ⇀

= cos + sinu⇀ π3 i ⇀ π

3 j ⇀

θ =

−9 · = − 27y⇀ y⇀

∥ ∥

⇀∥ ∥

= __________

Question 8: (1 point)

If and find the following.

= ____________

=____________

=____________

Question 9: (1 point)

Find the dot product.

= __________

∥ ∥ y

⇀∥ ∥

= ⟨− 5, 2⟩ ,u⇀ = ⟨4.3, 1.2⟩ ,v⇀ = ⟨− 1.9, 3.5⟩ ,w⇀

· ( + )u⇀ v⇀ w⇀

·v⇀ v⇀

6 ( · )u⇀ v⇀

⟨− 0.9, − 3.5⟩ · ⟨4.5, 2.7⟩